The sum of two integers is 54 and their difference is 10.

Solve for x first

X+y=54

X-y=10

Add

2x=64

Divide

X=64/2

X = 32

So now get one equation and substitute x to solve for y

32+y=54

Y=54-32

Y = 22

So your two numbers is 32 and 22.

To check substitute

32+22=54

32-22=10

They check