Albert Barnes Commentary Exodus 34:29

"And it came to pass, when Moses came down from mount Sinai with the two tables of the testimony in Moses` hand, when he came down from the mount, that Moses knew not that the skin of his face shone by reason of his speaking with him." — Exodus 34:29 (ASV)

The two tables of testimony - .

The skin of his face shone - . The brightness of the Eternal Glory, though Moses had witnessed it only in a modified manner (Exodus 33:22–23), was so reflected in his face that Aaron and the people were stricken with awe, and feared to approach him until he gave them words of encouragement.

The word translated “shine” is closely connected with a word translated “horn”; consequently, the Latin version and others have translated the verb as “to be horned.” From this translation of the word has arisen the popular representation of Moses with horns on his forehead, for example, in Michelangelo’s statue at Rome.