Let m and n are the numbers of sides of the two polygons.


Then your first equation is


((m-2)*180 - (n-2)*180 = 900,    or


(m-2) - (n-2) = 900/180 = 5,   or


m - n = 5.       (1)


Your second equation is


m + n = 25.      (2)


Add equations (1) and (2).


You get  2m = 5+25 = 30  ====>  m = 15.


Then from (2)  n = 25-15 = 10.


Answer.  15 and 10 sides.