We have x^2 + y^2 = 100 and x - y = 2. We have to solve these equations for x and y.
x - y = 2
=> (x - y)^2 =2^2
=> x^2 + y^2 - 2xy = 4
substitute x^2 + y^2 = 100
=> 100 - 2xy = 4
=> 2xy = 96
=> xy = 48
substitute x = 2 + y
=> y(2 + y) = 48
=> y^2 + 2y - 48 = 0
=> y^2 + 8y - 6y - 48 = 0
=> y(y + 8) - 6(y + 8) = 0
=> (y - 6)(y + 8) = 0
=> y = 6 and y = -8
for y = 6, x = 8
for y = -8, x = -6
The required solution is (-6, -8) and (8, 6)
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