Assuming that it was really |x+y|= 25, then, by the "parallelogram rule" for vector addtion, x+ y is the one diagonal of a parallelogram having sides x and y and x- y is the other diagonal. You can find the angle in the triangle with sides x, y, and x+y by using the cosine law on a triangle with sides of length 25, 13, and 17, then use the cosine law on a triangle with sides x, y, and x- y, and the same angle, to find the length of x-y.
Or you could use the fact that to argue that . You can easily find and and then find . Now use the fact that to find |x-y|.
In fact, do it both ways, as a check and really shock your teacher!