Problem: If Moses is the author of these passages, then why does he write about himself in the third person, rather than the first?
Solution: This objection is wrapped up in the authorship of the Pentateuch. However, here we might point out that other ancient biographies also spoke in the third person. For instance, Julius Caesar wrote the Gallic Wars and the Civil Wars in the third person. Xenophon wrote Anabasis in the third person. Jesus himself even spoke in the third person (Jn. 17:3; c.f. Daniel 7 and the book of Ezra). Moses probably wrote these accounts in the third person to let future Israelites know who was the central leader of Israel. An impersonal “I” wouldn’t explain this.
“These are that Aaron and Moses, to whom the Lord said, Bring out the children of Israel from the land of Egypt according to their armies. These are they which spake to Pharaoh king of Egypt, to bring out the children of Israel from Egypt: these are that Moses and Aaron. (Ex 6:26-27)
