The Impossible Puzzle

The Wikipedia Page.

The Puzzle itself:

Given are X and Y, two integers, greater than 1, are not equal, and their sum is less than 100. S and P are two mathematicians; S is given the sum X+Y, and P is given the product X*Y of these numbers.

• P says "I cannot find these numbers."
• S says "I was sure that you could not find them."
• P says "Then, I found these numbers."
• S says "If you could find them, then I also found them."

What are these numbers?

The Solution: X=4, Y=13