Let x and y represent the numbers and x>y

The smaller of two numbers is 4 less than the larger:

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

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x1 = 7

x2 = -3

For x = 7 we have y = 7 - 4 = 3. The two numbers are 7 and 3.

For x = -3 we have y = -3 - 4 = -7. The two numbers are -3 and -7.