Let x and y be the two unknown numbers. Let's make x the larger number. So x > y.
"The sum of two numbers is 76" means that when you add them together, you get 76, so
"their difference is 52" means that when you subtract them, you get 52, so
The system of equations is
We'll use this system to solve for x and y.
Start by adding the equations (add the left sides separately and the right sides separately)
x + y = 76
x - y = 52
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2x + 0y = 128
So that means 2x = 128 and isolating x (divide both sides by 2) gives us x = 64
Now we use x = 64 to find y. So we pick on any equation that has both x & y in it, plug in x = 64 and solve for y. I'm going to pick the first equation.
x+y=76
64+y=76
y=76-64
y=12
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So we've found that x = 64 and y = 12.
Therefore, the two numbers are 64 and 12.
Notice how 64+12 = 76 and how 64-12 = 52. So the answers check out.