Question 1081867
The quick answer: 36 and 63.
The fact that the digits add to 9 tells you both numbers are multiples of 9.
Multiples of 9 lesser than 99 are
09,18,27,36,45,54,63,72,81,90.
They come in pairs of one number and its reversed-digits twin.
Obviously, the ones in the middle of the list, 45 and 54, differ by 9.
The next pair, 36 and 63, has as difference of {{{3*9=27}}} .
The one after that differs by {{{5*9=54}}} , and so on
 
The show your work way:
If you have to show work, it is shorter to write equations than to explain reasoning in words.
From what I write below, feel free to skip anything that your teacher would not require.
{{{t}}}= the tens digit
{{{u}}}= the ones digit,
with {{{t>u}}}
{{{t+u=9}}} (because the sum of digits is 9)
{{{(10t+u)-(10u+t)=27}}} (because the value of the greater number is 10t+u, and the value of the other, reversed-digits number is 10u+t).
Simplifying,
{{{(10t+u)-(10u+t)=27}}}
{{{10t+u-10u-t=27}}}
{{{(10-1)*t+(1-10)*u=27}}}
{{{9t-9u=27}}}
{{{9(t-u)=27}}}
{{{t-u=27/9}}}
{{{t-u=3}}}
Then, {{{system(t+u=9,t-u=3)}}} ---> {{{system(t=6,u=3)}}}