The difference of the squares of two positive consecutive even integers is 28.

Find the integers. Use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

If x is the first even integer, then the next is x+2.

The difference of their squares is (x+2) ^2 - x^2, and this is equal to 28.

Expanding:

x^2 + 4x + 4 - x^2 = 28

4x + 4 = 28

4x = 24

x = 6

x+2 = 8

Therefore, the two numbers are 6 and 8.