Question 551147
let the two digit number is xy
The sum of the digits of a certain two digit number is 8
so, x+y=8
we have possibilities (1,7),(2,6)(3,5),(4,4) vice versa we cany take because,if the number formed by interchanging the digits is subtracted from the original number the result is -18. 
first take, x=1,y=7
x+y=7 
1+7=8
8=8
satisfies one condition,but we have to check other condition.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18. 
Which means, xy-yx=-18
17-71=-18 not satisfied so x=1,y=7 are not. 
take, x=2,y=6
x+y=8
2+6=8
8=8
satisfies one condition,but we have to check other condition also.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18. 
xy-yx=-18
26-62=-18  not satisfies the condition.

take, x=3,y=5
x+y=8
3+5=8
8=8
satisfies one condition,but we have to check other condition also.i.e.,If the number formed by interchanging the digits is subtracted from the original number the result is -18. 
xy-yx=-18
35-53=-18   satisfies the condition.
so , solutions are x=3,y=5 
original number =35----->answer