The sum of two numbers is 43 and their difference is 21. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 43. In other words, x plus y equals 43 and can be written as equation A:

**x + y = 43**

The difference between x and y is 21. In other words, x minus y equals 21 and can be written as equation B:

**x - y = 21**

Now solve equation B for x to get the revised equation B:

**x - y = 21**

x = 21 + y

x = 21 + y

Then substitute x in equation A from the revised equation B and then solve for y:

**x + y = 43**

21 + y + y = 43

21 + 2y = 43

2y = 22

y = 11

21 + y + y = 43

21 + 2y = 43

2y = 22

y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

**x + y = 43**

x + 11 = 43

X = 32

x + 11 = 43

X = 32

Summary: The sum of two numbers is 43 and their difference is 21. What are the two numbers? Answer: 32 and 11 as proven here:

**Sum: 32 + 11 = 43**

Difference: 32 - 11 = 21

Difference: 32 - 11 = 21

**Sum Difference Calculator**

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**The Sum of Two Numbers is 43 and Their Difference is 22**

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