let 'x' and 'y' be the two numbers

two number differ by 6

x - y = 6

y = x - 6

the differences of thier square root is 120

x^2 - y^2 = 120

plug y = x - 6 into the last equation

x^2 - (x - 6)^2 = 120

by solving we find

x = 13

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13 - 6 = 7

the two numbers are 13 and 7.