The sum of two numbers is 24. The difference of their squares is 144. Find the two numbers?

Let the two numbers be x and y.

According to the given conditions:
x + y = 24
x^2 - y^2 = 144

We can rewrite the second equation as:
(x + y)(x - y) = 144
Substitute x + y = 24 into the equation:
24(x - y) = 144
x - y = 6

Now we have a system of two equations:
x + y = 24
x - y = 6

Adding the two equations together:
2x = 30
x = 15

Substitute x = 15 back into x + y = 24:
15 + y = 24
y = 9

Therefore, the two numbers are 15 and 9.