Let 'x' and 'y' represent the positive integers, x >0, y>0.

y = 2x - 4

The sum of their squares is 100 means:

x^2 + y^2 = 100

Plug y = 2x - 4 into the last equation:

x^2 + (2x - 4)^2 = 100

........

click here to see the equation solved for x

........

x = 6

We need to ignore the negative solution -2.8 since x can only be positive.

y = 2*6 - 4

y = 12 - 4

y = 8

Indeed 6^2 + 8^2 = 36 + 64 = 100.

The two positive integers are 6 and 8.