Problème (connu?)

Homer gives mathematicians Patty and Selma each a different integer, not known to the other or to you. Homer tells them, within each other's hearing, that the number given to Patty is the product ab of the positive integers a and b, and that the number given to Selma is the sum a + b of the same numbers a and b, where b > a > 1. He doesn’t, however, tell Patty or Selma the numbers a and b.

The following (honest) conversation then takes place:
Patty: "I can’t tell what numbers a and b are."
Selma: "I knew before that you couldn’t tell."
Patty: "In that case, I now know what a and b are."
Selma: "Now I also know what a and b are."

Supposing that Homer tells you (but neither Patty nor Selma) that neither a nor b is greater than 20, find a and b, and prove your answer can result in the conversation above.