The sum of the squares of two positive integers is 100 and the difference of their squares is 28. What is the sum of the number?

Suppose those integers are A and B and A is greater than B.

Then,as per first condition ,A2+B2=100……………Equation-1.

Next,as per second condition,A2 - B2=28……..Equation-2.

Now,On adding the Eqn.-1 &2,we get

2 x A2=128

Hence,A2=64,So A=8.

Putting this value in Eqn-1,we get

B2=100–64=36,So B=6.

Hence,their sum is 8+6=14.