I suggest you study a little bit the controversy of Barlaam, a former Orthodox who was condemned by the Fifth General (Ecumenical?) Council of Constantinople and embraced Catholicism for that reason. While there are RCs who did or do approve of the Eastern Orthodox doctrine of Hesychasm as explained by st. Gregory Palamas, the RCC has made no attempt to explain this and still continues to ignore the subject. Only recently, Pope John Paul II has recognized the problem of distinguishing between God's trascendence (His essence) and God's immanence (His energies) without breaking divine monism/simplicity as expressed in the Fourth Lateran Council. The theology of st. Gregory of Palamas, supported by Holy Orthodoxy, has already taken a stand on the matter from a dogmatic point of view, and can show to the RCC an alternative to a great variety of positions which vary from:
1) Understanding God without distinguishing His transcendence and immanence, as did Thomas Aquinas who said that Existence and Essence in God are one and the same thing. In Orthodoxy that would be admitting that God's ESSENCE contaminates with creation as in a sort of Pantheism.
2) Correcting the aforemantioned position saying that God's energies are created, as former Orthodox Barlaam did before and after becoming a RC bishop. This way, God sends His created energies - and thus grace - preserving His essence intact, but at the same time denying that God becomes present in the faithful (and in the saints especially) when He sends His grace. One of the conclusions of Barlaam was even that God's light, or glory, must have been created. This position implies that the mystics only see these energies, while the saints in heaven enjoy God's pure essence.
3) Preserving the Orthodox position which explains God as both unchangeable in His transcendental essence and dynamic in His immanent energies. This way, both the mystics and the saints in heaven have an experience of God's energies which are indeed God in his dynamis, what the Bible calls the "face of God". From a technical point of view, Moses saw God "face to face", but the Gospel of st. John says that "Nobody at any time has ever seen God: but the Unbegotten Son has revealed Him". From a Catholic perspective, as sanctioned in the writings of Augustine of Hippo, the light witnessed by Moses and by the three apostles at Transfiguration (which the Orthodox call "Tabor Light") was created, and thus the only light which will be visible is the Beatific Vision of God's essence. This could be used as the only defence of Barlaam's position, but the statement of John doesn't demonstrate anything, or better, it can easily be disproved by the words "but the Unbegotten Son, who is the bosom of the Father, has revealed Him". In fact, both the same apostle John with Peter and James, but also Moses himself, clearly saw God in His uncreated glory. This is possible because, from an Orthodox perspective, "the Son of God" has revealed to these men the Uncreated Glory of God before their deaths. In fact, the three apostles saw Jesus in His glory on Tabor, and Moses saw God as the "Angel of the Face (or "of the presence") of the Lord" which is Jesus before His incarnation.
As a Roman Catholic, you might have a choice to go against the major tendency (which is not dogmatized, but implied) of your Church and witness an uncreated Energy as distinct but inseparable from God's essence, preserving intact the monism/simplicity of God.
In Christ, Alex