The sum of the squares of two positive integers is 100 and the difference between their square is 28. The sum of the numbers is>

Let the integers be x and y. Given x² + y² = 100 and x² - y² = 28. Adding these equations yields 2x² = 128, so x = 8. Substituting x² = 64 into the first equation gives y² = 36, so y = 6. The sum is 8 + 6 = 14.