let those numbers be a and b
a+b = 25 -----(i)
ab = 154 -----(ii)
from (ii)
a = 154/b
by substituting for "a" in (i)
a + b = 25
(154/b) + b = 25
( 154 + b^2)/b = 25
154 + b^2 = 25b
154 + b^2 -25b =0
now, arrange the terms
b^2 - 25b + 154 = 0
b^2 - 14b - 11b + 154 =0
b (b-14) -11 (b-14) =0
(b-11)(b-14)= 0
now find the value for b
b -11 =0
b = 11
and
b-14=0
b = 14
b equals either 14 or 11
and a = 154/b
if b = 11 then, a = 154/11 = 14
if b = 14 then, a = 154/14 = 11
so, the value of a and b are 11 and 14.
so, those numbers are 11 and 14.