32 And now let us enquire whether elsewhere than in the case of Hagar the Angel of God has been discovered to be God Himself. He has been so discovered, and found to be not only God, but the God of Abraham and of Isaac and of Jacob. For the Angel of the Lord appeared to Moses from the bush; and Whose voice, think you, are we to suppose was heard? The voice of Him Who was seen, or of Another? There is no room for deception; the words of Scripture are clear: And the Angel of the Lord appeared unto him in a flame of fire from a bush, and again, The Lord called unto him from the bush, Moses, Moses, and he answered, What is it?
And the Lord said, Draw not near hither, put off your shoes from off your feet, for the place whereon you stand is holy ground. And He said unto him, I am the God of Abraham, and the God of Isaac, and the God of Jacob</em>. He who appeared in the bush speaks from the bush; the place of the vision and of the voice is one; He Who speaks is none other than He Who was seen. He Who is the Angel of God when the eye beholds Him is the Lord when the ear hears Him, and the Lord Whose voice is heard is recognised as the God of Abraham, and of Isaac, and of Jacob.
When He is styled the Angel of God, the fact is revealed that He is no self-contained and solitary Being: for He is the Angel of God. When He is designated Lord and God, He receives the full title which is due to His nature and His name. You have, then, in the Angel Who appeared from the bush, Him Who is Lord and God.
Source: On the Trinity (New Advent)