The sum of two numbers is 63. The larger number minus the smaller number is 9.

Let's call the two numbers x and y, with x being the larger number and y being the smaller number.

From the given information, we have the following equations:
1) x + y = 63
2) x - y = 9

Now, we can solve these two equations simultaneously. Adding the two equations, we get:
x + y + x - y = 63 + 9
2x = 72
x = 36

Substitute the value of x back into equation 1 to find y:
36 + y = 63
y = 63 - 36
y = 27

Therefore, the two numbers are 36 and 27.