One number exceeds another by 24. The sum of the numbers are 58. What are the numbers?

To find the numbers, let's set up a system of equations. Let's assume the first number is x and the second number is y.

According to the problem, "One number exceeds another by 24," we can write the equation:
x = y + 24

The problem also states, "The sum of the numbers is 58," so we can write the equation:
x + y = 58

Now, solve the system of equations using substitution or elimination to find the values of x and y.

Using substitution:
Substitute the value of x from the first equation into the second equation:
(y + 24) + y = 58
2y + 24 = 58
2y = 58 - 24
2y = 34
y = 34/2
y = 17

Now, substitute the value of y back into the first equation to find x:
x = 17 + 24
x = 41

So, the numbers are x = 41 and y = 17.