When the Lord revealed Himself to Moses on Mount Sinai, He did not show Moses His face. Still, the glory of the Lord was so great that Moses himself reflected in. Coming down from Mount Sinai, his face shone so brightly that he had to cover himself with a veil.
The radiance of Moses reminds us of the Transfiguration, when Moses and Elijah appeared with Christ on Mount Tabor. This radiance reflects an inner transformation that all Christians are called to. The Holy Spirit, through His grace, transforms us into the likeness of God.
Exodus 33:7-11, 18-23; 34:5-9, 29-35
Moses also taking the tabernacle, pitched it without the camp afar off, and called the name thereof, The tabernacle of the covenant. And all the people that had any question, went forth to the tabernacle of the covenant, without the camp.
And when Moses went forth to the tabernacle, all the people rose up, and every one stood in the door of his pavilion, and they beheld the back of Moses, till he went into the tabernacle. And when he was gone into the tabernacle of the covenant, the pillar of the cloud came down, and stood at the door, and he spoke with Moses. And all saw that the pillar of the cloud stood at the door of the tabernacle. And they stood, and worshipped at the doors of their tents. And the Lord spoke to Moses face to face, as a man is wont to speak to his friend. And when he returned into the camp, his servant Josue the son of Nun, a young man, departed not from the tabernacle.
And he said: Shew me thy glory. He answered: I will shew thee all good, and I will proclaim in the name of the Lord before thee: and I will have mercy on whom I will, and I will be merciful to whom it shall please me. And again he said: Thou canst not see my face: for man shall not see me and live. And again he said: Behold there is a place with me, and thou shalt stand upon the rock. And when my glory shall pass, I will set thee in a hole of the rock, and protect thee with my right hand, till I pass: And I will take away my hand, and thou shalt see my back parts: but my face thou canst not see.
And when the Lord was come down in a cloud, Moses stood with him, calling upon the name of the Lord. And when he passed before him, he said: O the Lord, the Lord God, merciful and gracious, patient and of much compassion, and true, Who keepest mercy unto thousands: who takest away iniquity, and wickedness, and sin, and no man of himself is innocent before thee. Who renderest the iniquity of the fathers to the children, and to the grandchildren, unto the third and fourth generation. And Moses making haste, bowed down prostrate unto the earth, and adoring, Said: If I have found grace in thy sight: O Lord, I beseech thee, that thou wilt go with us, (for it is a stiffnecked people,) and take away our iniquities and sin, and possess us.
And when Moses came down from the mount Sinai, he held the two tables of the testimony, and he knew not that his face was horned from the conversation of the Lord. And Aaron and the children of Israel seeing the face of Moses horned, were afraid to come near. And being called by him, they returned, both Aaron and the rulers of the congregation. And after that he spoke to them. And all the children of Israel came to him: and he gave them in commandment all that he had heard of the Lord in mount Sinai.
And having done speaking, he put a veil upon his face. But when he went in to the Lord, and spoke with him, he took it away until he came forth, and then he spoke to the children of Israel all things that had been commanded him. And they saw that the face of Moses when he came out was horned, but he covered his face again, if at any time he spoke to them.
- Source: Douay-Rheims 1899 American Edition of the Bible (in the public domain)

