Two people, named S and P, are talking about two numbers x and y, with x and y both integers greater than or equal to 2. S knows their sum (x+y), while P knows their product (xy); however, initially NEITHER knows x and y.

S: Hey P! I don’t know what the numbers are.
P: I’m not surprised. I KNEW you didn’t know. However, I too don’t know.
S: You don’t? Really! Then I know what the numbers are!

What are the two numbers?

Communicated by Kathryn Sievers.