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

Two numbers differ by 10:

y - x = 10

y = x + 10

They have a product of 704:

xy = 704

plug y = x + 10 into the last equation

x(x + 10) = 704

by solving we find

x1 = 22

x2 = - 32

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for x = 22 we have y = 22 + 10 = 32

for x = - 32 we have y = - 32 + 10 = - 22

there are 2 solutions:

First solution: the numbers are 22 and 32.

Second solution: the numbers are - 32 and -22.