What I am curious about is how/why the East believed it was possible to attain such a specific knowledge of the nature of God (past the dogma of the Holy Trinity), such as that He consists of an essence and energies.
An excellent question. I would suggest it is not about specific knowledge of His nature or how God is constituted; according to Orthodoxy the only way to know God is to love Him.
"He that loveth not knoweth not God; for God is love." -1 Jn 4:8
"Even the statement "God exists" must be countered with the apophatic statement that God's existence is altogether different than any existence that we can imagine." http://orthodoxwiki.org/Cataphatic_theology
"For we explain not what God is [i.e. God's nature or essence] but candidly confess that we have not exact knowledge concerning Him. For in what concerns God to confess our ignorance is the best knowledge" (St. Cyril , Catechetical Homilies
, VI.2 (c. AD 335).
Knowledge of God is neither apart from loving God (1 Jn 4:8) or the Son's revealing of God: "No one knows the Father except the Son and those to whom the Son chooses to reveal him" (Matt 11:27; cf. John 14:21: "He who has My commandments and keeps them is the one who loves Me; and he who loves Me will be loved by My Father, and I will love him and will disclose Myself to him").
The God of Moses related to Moses personally, whereas e.g. Aristotle related a concept of God through the intellect alone. As St. John tells us we cannot know God except by loving Him, St. Paul tells us we cannot know Him through worldly wisdom: "For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. Jews demand miraculous signs and Greeks look for wisdom, but we preach Christ crucified: a stumbling block to Jews and foolishness to Gentiles,but to those whom God has called, both Jews and Greeks, Christ the power of God and the wisdom of God" (1 Corinthians 1:21ff).
"Blessed are the pure in heart, for they shall know God" -Matt 5:8
"Christ Himself revealed to us the method. He told us that not only are we capable of exploring God, but we can also live with Him, become one with Him. And the organ by which we can achieve that is neither our senses nor our logic but our hearts" -Fr. Maximos, in The Mountain of Silence
Orthodox tradition and experience draws a definite distinction between experience and ideological belief.
God may be seen in creation (Rom 1) but not through natural reason apart from revelation (natural revelation vs. natural theology). One can become suddenly darkened with respect to this natural revelation (Rom 1:21 -notice St. Paul emphasizes it is the hearts of those who choose to reject the revealing God that are first darkened).
“Why is the truth, it would seem, revealed to some and not to others? Is there a special organ for receiving revelation from God? Yes, though usually we close it and do not let it open up: God’s revelation is given to something called a loving heart.” -Seraphim Rose, God's Revelation to the Human Heart
"God is called light, Who transcends all light, because He illumines us; and life, Who is beyond all life, because He vivifies us. Shining around us all, and encircling and cherishing us with the glory of His divinity, He is called raiment, and so we saw that we clothe ourselves with Him Who is intangible in every way and Who cannot be grasped. Uniting Himself without mingling with our soul, and making it all as light, He is said to indwell us and, uncircumscribed, become circumscribed." -St. Symeon the New Theologian
Following is an excellent account of how this is discribed in the Orthodox tradition by Archbishop Hilarion (Alfeyev):
Each of God’s revelations in the Old Testament bear a personal nature. God is revealed to humanity not as an abstract force, but as a living Being, Who can speak, hear, see, think and help. God takes a vital and active part in the life of the Israelites. When Moses leads the people out of Egypt into the Promised Land, God Himself goes ahead of them in the form of a column of fire. God abides among the people, converses with them and lives in the house that they built for Him. When King Solomon completed the building of the Temple, he called upon God to live there. God, Who abides in darkness, Who is surrounded by great mystery, Whom heaven and earth, that is, the visible and invisible world, cannot contain, comes down to people and lives where they want Him to live, where they have set aside a place for Him.
This is the most striking thing about the religion of revelation: God remains under the veil of a mystery, remains unknown and yet at the same time He is so close to people that they can call Him ‘our God’ and ‘my God’. It is here that we encounter the gulf between Divine revelation and the achievements of human thought: the God of the philosophers remains abstract and lifeless, whereas the God of revelation is a living, close and personal God. Both ways lead us to understand that God is incomprehensible and that He is a mystery; yet philosophy abandons us at the foothills of the mountain, forbidding us to ascend further, whereas religion leads us up to the heights where God abides in darkness, it draws us into the cloud of unknowing where beyond all words and rational deductions it opens up before us the mystery of God.
THE DIVINE NAMES
‘How can we speak of the Divine names? How can we do this if the Transcendent surpasses all discourse and all knowledge..? How can we enter upon this undertaking if the Godhead is superior to being and is unspeakable and unnameable?’, says Dionysius the Areopagite. At the same time, God, being totally transcendent, is present in the created world and revealed through it. All creation longs for God, and more especially, we humans crave for knowledge of Him. Therefore God is to be praised both ‘by every name’ and ‘as the Nameless One’. Nameless in His essence, God is variously named by humanity when He reveals Himself to us.
Some of the names attributed to God emphasize His superiority over the visible world; His power, dominion and kingly dignity. The name Lord (Greek, Kyrios) signifies the supreme dominion of God not only over His chosen people, but also over the whole world. The name of Almighty (Greek, Pantokrator) signifies that God holds all things in His hand; He upholds the world and its order.
The names Holy, ‘Holy Place’, Holiness, Sanctification, Good and Goodness indicate that God not only contains within Himself the whole plenitude of goodness and holiness, but He also pours out this goodness onto all of His creatures, sanctifying them.
In Holy Scripture there are other attributions to God: Wisdom, Truth, Light, Life, Salvation, Atonement, Deliverance, Resurrection, Righteousness, Love. There are in Scripture a number of names for God taken from nature. These do not attempt to define either His characteristics or His attributes, but are rather symbols and analogies. God is compared with the sun, the stars, fire, wind, water, dew, cloud, stone, cliff and fragrance. Christ Himself is spoken of as Shepherd, Lamb, Way, Door. All of these epithets, simple and concrete, are borrowed from everyday reality and life. But, as in Christ’s parables of the pearl, tree, leaven and seeds, we discern a hidden meaning that is infinitely greater and more significant.
Holy Scripture speaks of God as a being with human form having a face, eyes, ears, hands, shoulders, wings, legs and breath. It is said that God turns around and turns away, recollects and forgets, becomes angry and calms down, is surprised, sorrows, hates, walks and hears. Fundamental to this anthropomorphism is the experience of a personal encounter with God as a living being. In order to express this experience we have come to use earthly words and images.
‘FATHER’ AS A DIVINE NAME
‘Father’ is the traditional, biblical name for God. His children are the people of Israel: ‘For Thou art our Father, though Abraham does not know us and Israel does not acknowledge us; Thou, O Lord art our Father, our Redeemer from of old is Thy name’ (Is.63:16). The fatherhood of God is, of course, not a matter of maleness for there is no gender in the Divinity. It is important to remember, however, that the name ‘Father’ was not simply applied by humans to the Divinity: it is the very name with which God opened Himself to the people of Israel. Male imagery was not therefore imposed on God, rather God Himself chose it in His revelation to humans (cf. 2 Sam.7:14; 1 Chron.17:13; Jer.3:19; 31:9). The three Persons of the Holy Trinity bear the names Father, Son and Holy Spirit, where the name Son belongs to the eternal Logos of God, Who was incarnate and became man. In Semitic languages where the word for Spirit (Hebrew ruah, Syriac ruha) is feminine, female imagery is applied to the Holy Spirit. Both the Hebrew and the Greek terms for the Wisdom of God (Hebrew hokhma, Greek sophia) are feminine: this opens the possibility of applying female imagery to the Son of God, Who is traditionally identified with the Wisdom. With this exception, for both Father and Son exclusively male imagery is used in the Eastern tradition.
The Orthodox normally oppose modern attempts to change traditional biblical imagery by making God-language more ‘inclusive’ and referring to God as ‘mother’, and to His Son as ‘daughter’, or using the generic terms ‘parent’ and ‘child’. For the Orthodox, the full understanding of motherhood is embodied in the person of the Mother of God, whose veneration is not merely a custom or cultural phenomenon, but a church dogma and an essential part of spirituality. It is therefore not a matter of cultural difference between the Orthodox and the Roman Catholics on the one hand, and the Protestants on the other, that the former venerate the Mother of God, while the latter pray to ‘God the Mother’. It is a serious dogmatic difference. Moreover, it is not simply stubbornness on the part of the Orthodox when they reject changing biblical God-language, but rather a clear understanding of the fact that the entire spiritual, theological and mystical tradition of the Church undergoes irrecoverable alterations when the traditional set of the divine names and images is changed.
Indeed, any name can be applied to the Divinity, while none can describe it. All names used for God in biblical and Orthodox traditions are aimed at grasping the mystery which is beyond names. Nevertheless, it is crucially important to remain with biblical God-language and not replace it with innovative forms. All names for God are anthropomorphic. Yet there is a difference between biblical anthropomorphism, which is based on the experience of the personal God in His revelation to humans, and the pseudo-anthropomorphism of modern theologians who, by introducing the notion of gender into the Divinity, speak of God as ‘He-She’, or ‘Our Mother and Father’.
"When discussing the names of God, we inevitably conclude that not one of them can give us a complete idea of who He is. To speak of the attributes of God is to discover that their sum total is not God. God transcends any name. If we call Him being, He transcends being, He is supra-being. If we ascribe to Him righteousness and justice, in His love He transcends all justice. If we call Him love, He is much more than human love: He is supra-love. God transcends all attributes that we are capable of ascribing to Him, be it omniscience, omnipresence or immutability. Ultimately we arrive at the conclusion that we can say nothing about God affirmatively: all discussion about Him remains incomplete, partial and limited. Finally we come to realize that we cannot say what God is, but rather what He is not. This manner of speaking about God has received the name of apophatic (negative) theology, as opposed to cataphatic (affirmative) theology.
"The traditional image of Moses ascending Mount Sinai to God, surrounded in darkness, inspired both St Gregory of Nyssa and Dionysius the Areopagite to speak about the divine darkness as a symbol of God’s incomprehensibility. To enter the divine darkness is to go beyond the confines of being as understood by the intellect. Moses encountered God but the Israelites remained at the foot of the mountain, that is, within the confines of a cataphatic knowledge of God. Only Moses could enter the darkness; having separated himself from all things, he could encounter God, Who is outside of everything, Who is there where there is nothing. Cataphatically we can say that God is Light, but in doing so we liken God to sensible light. And if it is said about Christ transfigured on Mount Tabor that ‘his face shone like the sun, and his garments became white as light’ (Matt.17:2), then the cataphatic notion of ‘light’ is used here symbolically, since this is the uncreated light of the Divinity that transcends all human concepts of light. Apophatically we can call the Divine light, the supra-light or darkness. Thus the darkness of Sinai and the light of Tabor are one and the same.
"In our understanding of God we often rely upon cataphatic notions since these are easier and more accessible to the mind. But cataphatic knowledge has its limits. The way of negation corresponds to the spiritual ascent into the Divine abyss where words fall silent, where reason fades, where all human knowledge and comprehension cease, where God is. It is not by speculative knowledge but in the depths of prayerful silence that the soul can encounter God, Who is ‘beyond everything’ and Who reveals Himself to her as in-comprehensible, in-accessible, in-visible, yet at the same time as living and close to her — as God the Person.
Getting back to your excellent question, Bishop Kallistos Ware explains with respect to God's energies as opposed to His essence that this is not about, to borrow from your original question, things like specific knowledge of the nature of God or constitution:
From Bishop Kallistos Ware, The Orthodox Way
(NY: SVS, 2002)ESSENCE AND ENERGIES
To indicate the two “poles” of God’s relationship to us —unknown yet well known, hidden yet revealed— the Orthodox tradition draws a distinction between the essence, nature or inner being of God, on the one hand, and his energies, operations or acts of power, on the other.
“He is outside all things according to his essence,” writes St Athanasius, “but he is in all things through his acts of power.”12 “We know the essence through the energy”, St Basil affirms. “No one has ever seen the essence of God, but we believe in the essence because we experience the energy.”13 By the essence of God is meant his otherness, by the energies his nearness. Because God is a mystery beyond our understanding, we shall never know his essence or inner being, either in this life or in the Age to come. If we knew the divine essence, it would follow that we knew God in the same way as he knows himself; and this we cannot ever do, since he is Creator and we are created. But, while God’s inner essence is for ever beyond our comprehension, his energies, grace, life and power fill the whole universe, and are directly accessible to us.
The essence, then, signifies the radical transcendence of God; the energies, his immanence and omnipresence. When Orthodox speak of the divine energies, they do not mean by this an emanation from God, an “intermediary” between God and man, or a “thing” or “gift” that God bestows. On the contrary, the energies are God himself in his activity and self-manifestation. When a man knows or participates in the divine energies, he truly knows or participates in God himself, so far as this is possible for a created being. But God is God, and we are human; and so, while he possesses us, we cannot in the same way possess him.
Just as it would be wrong to think of the energies as a “thing” bestowed on us by God, so it would be equally misleading to regard the energies as a “part” of God. The Godhead is simple and indivisible, and has no parts. The essence signifies the whole God as he is in himself; the energies signify the whole God as he is in action. God in his entirety is completely present in each of his divine energies. Thus the essence-energies distinction is a way of stating simultaneously that the whole God is inaccessible, and that the whole God in his outgoing love has rendered himself accessible to man.
By virtue of this distinction between the divine essence and the divine energies, we are able to affirm the possibility of a direct or mystical union between man and God—what the Greek Fathers term the theosis of man, his “deification”—but at the same time we exclude any pantheistic identification between the two: for man participates in the energies of God, not in the essence. There is union, but not fusion or confusion. Although “oned” with the divine, man still remains man; he is not swallowed up or annihilated, but between him and God there continues always to exist an “I— Thou” relationship of person to person.
Such, then, is our God: unknowable in his essence, yet known in his energies; beyond and above all that we can think or express, yet closer to us than our own heart. Through the apophatic way we smash in pieces all the idols or mental images that we form of him, for we know that all are unworthy of his surpassing greatness. Yet at the same time, through our prayer and through our active service in the world, we discover at every moment his divine energies, his immediate presence in each person and each thing. Daily, hourly we touch him. We are, as Francis Thompson said, “in no strange land.” All around us is the “many-splen-doured thing”; Jacob’s ladder is “pitched betwixt heaven and Charing Cross”:
O world invisible, we view thee,
O world intangible, we touch thee,
O world unknowable, we know thee,
Inapprehensible, we clutch thee.
In the words of John Scotus Eriugena, “Every visible or invisible creature is a theophany or appearance of God.” The Christian is the one who, wherever he looks, sees God everywhere and rejoices in him. Not without reason did the early Christians attribute to Christ this saying: “Lift the stone and you will find me; cut the wood in two and there am I.”
I hope some of this is might be helpful.