A neat problem

First of all, apologies for being out of radar for so long. I have been working hard on creating something new and it is close to where I want it to be. Details on that later.

For now, let me stimulate your grey cells with this smashing problem a friend at work posted to us who travel together in the evening cab. Last Friday, we spent an hour trying to make the just the first moves to solve this problem.

There are two guys and two numbers. Guy1 knows only the product of the numbers while Guy2 knows only the sum. Both numbers are known to be between 2 and 99 inclusive. The following conversation ensues:
Guy1-> I don't know what the numbers are.
Guy2-> I know that you don't know what the numbers are.
Guy1-> Now I know what the numbers are.
Guy2-> Now even I know what the numbers are.
Question: What are the numbers?

And here's the solution.

Enjoy!