let 'x' and 'y' be the numbers

The sum of two numbers is 25

x + y = 25

One number is 8 less than twice, the other number

y = 2x - 8

we plug y = 2x - 8 into x + y = 25

x + 2x - 8 = 25

to find

x = 11

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y = 2*11 - 8

y = 14

the two numbers are 11 and 14.