Your starting equations are

    x + y = 25           (1)

     +  =         (2)


From equation (2)

     ] 

    4*(x+y) = xy


Replace here x+y by 25, based on equation (1).  You will get

    xy = 4*25 = 100.


So, you have two equations

    x + y = 25       (3)

     xy   = 100      (4)


From here, the  ANSWER  is OBVIOUS:  (x,y) = (20,5)  or  (5,20).      (*)


If you want to get formal solution, express  x = 25-y from (3) and substitute it to (4).  You will get

    (25-y)*y = 100

    25y - y^2 = 100

    y^2 - 25y + 100 = o

    (y-20)*(y-5) = 0

giving two possibilities  y= 20  or  y= 5.


They lead to answer (*): the numbers are 5 and 20, in any order.