Find the two numbers whose sum is 51 and whose difference is 13?

Let's call the two numbers x and y. We can set up a system of equations based on the given information: x + y = 51 and x - y = 13. By solving this system simultaneously, we can find the values of x and y. Adding the two equations together, we get 2x = 64, so x = 32. Substituting x back into the first equation, we find that y = 19. Therefore, the two numbers are 32 and 19.