The sum of two numbers is 21 and their difference is 13

The two numbers are 17 and 4.

Step-by-step explanation:

Sum:

17+4 = 21

Difference

17-4 = 13

Set up 2 equations:

x + y = 21

Y - x = 13

Rewrite the last one as y = 13 + x

Now replace y in the first one:

X + (13 + x) = 21

Simplify:

2x + 13 = 21

Subtract 14 from both sides:

2x = 8

Divide both sides by 2:

X = 4

Now you have x solve for y:

Y = 13 + x = 13 + 4 = 17

The numbers are 4 and 17