Guess the numbers
Two mathematicians are placed in two rooms and one is given the sum of two
distinct numbers between 2 and 99 (2 and 99 excluded) and the other is given
the product of same two numbers. They both come out of the room and the
following conversation takes place.

Mathematician with product : "I don't know the two numbers".
Mathematician with sum : "I know, you won't know the two numbers".
Mathematician with product : "Now, I know the numbers".
Mathematician with Sum : "Now, I too know the numbers".

What are the numbers and how did they find it out ?