The sum of two numbers is 56, and their difference is 10. What are the numbers?

There are two equations hidden in the language here:

a + b = 56 and a - b = 10.

if you do (a+b) + (a-b) then you get:

(a+b) + (a-b) = 66 = a + b + a - b

The b's cancel, so you get 2a = 66, which means a = 33. You can use this to solve for b in one of the above equations by plugging in a = 33 and figuring out what b has to be. Then you will have your two numbers.

X + y = 56

x - y = 10 so x = y + 10

y + 10 + y = 56

2y + 10 = 56

2y = 56 - 10

2y = 46

y = 46/2

y = 23

x = y + 10 = 23 + 10 = 33

Answer: The numbers are 23 and 33

Proof:

sum: 23 + 33 = 56

difference: 33 - 23 = 10