Let's call the smaller number "x". Since the larger number exceeds the smaller number by 1, we can call the larger number "x + 1".
The problem tells us that the sum of the numbers is 25, so we can set up an equation:
x + (x + 1) = 25
Simplifying and solving for x:
2x + 1 = 25
2x = 24
x = 12
So the smaller number is 12. To find the larger number, we can use x + 1:
x + 1 = 12 + 1 = 13
So the larger number is 13.
Therefore, the two numbers are 12 and 13.