Hi,         

Let (x-10) and x represent the smaller and larger number respectively

Question States***

  (x-10)^2 + x^2 = 250

Solving for x

 x^2 - 20x + 100 + x^2 = 250

  2x^2 -20x -150 = 0 

  2(x^2 - 10x - 75) = 0

factoring

(x-15)(x +5) = 0 Note:SUM of the inner product(-15*x) and the outer product(5x) = -10x

(x-15)= 0

   x = 15, the larger number,smaller number is  5 

(x +5) = 0

   x = -5, the larger number, -15 the smaller number

CHECKING our Answers

 |smaller|^2 + |larger|^2 = 250 

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