Who was present and who told Matthew about the conversation Jesus had with the devil when He was tempted?

In Matthew 4: 1-11 Jesus was tempted in the wilderness. What is the source for the Apostle Matthew claiming the devil had a conversation with Jesus?  Was it a dream? Revelation?  Someone else who told Mathew? Was anyone else present with Jesus? Or did Jesus relay the conversation he had with the devil and if so, to whom and when?  
Thank you and God bless.

Clarify • Share • Report • Asked February 01 2015 • John Sheridan