A puzzle for your enjoyment

The professor says to Paula and Sam: I'm thinking of two whole numbers, x and y such that 1 < x < y and x+y < 100. I'm going to tell Paula the product of the two numbers and Sam the sum of the two numbers, which he then does.

Paula says: "I don't know the two numbers.".
Sam says: "I already knew that."
Paula says: "I know the two numbers."
Sam says: "So do I."

You can assume that everyone tells the truth throughout the conversation. What are the two numbers?