система   y = 4+x

                 x^2-2xy-y^2 = 14

уравнение    x^2-2x(4+x)-(4+x)^2 = 14

                      x^2-8x-2x^2-16-8x-x^2 = 14

                      -2x^2-16x-16-14 = 0

                      -2x^2-16x-30 = 0

                       x^2+8x+15 = 0

                      D = 64-4*15 = 4

                      x1 = (-8+2)/2 = -3

                       x2 = (-8-2)/2 = -5

находим у        

  у1 = 4-3 = 1

  у2 = 4-5 = -1

Ответ:  (-3;1),(-5;-1)