Question 1099464
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{{{x^2 - y^2}}} = 315  ====>

(x-y)*(x+y) = 315  ====>  replace (x-y) by 35, based on the condition. You will get

35*(x+y) = 315  ====>  x + y = {{{315/35}}} = 9.


Thus you reduced the given non-linear system to the simple LINEAR one, consisting of two equations

x - y = 35,
x + y =  9.
-------------------Add the two equations. You will get

2x = 35 + 9 = 44  ====>  x = {{{44/2}}} = 22.


One number is 22.  Then the other is  y = 22 - 35 = -13.


<U>Check</U>.  {{{22^2-(-13)^2}}} = 315.  ! Correct !


<U>Answer</U>.  The numbers are  22  and  -13.
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