Let x and y represent the integers and x>y

One integer is 4 less than another:

y = x - 4

The sum of their squares is 58:

x^2 + y^2 = 58

Plug y = x - 4 into the last equation:

x^2 + (x - 4)^2 = 58

........

........

x1 = 7

x2 = -3

For x = 7 we find y = 7 - 4 = 3, the two integers are 7 and 3.

For x = -3 we find y = -3 - 4 = -7, the two integers are -3 and -7.