Question 981507
The result of the two digits being equal means this is a multiple of 11;
so use an extra variable, n, for either of these resulting digits.
Your multiple of 11 is some 11*n, and n must be a digit.


Your unknown number, {{{10t+u}}};
t for your tens, u for your ones.


Your transcribed information will then be
{{{system(t+u=10,10t+u-8=11n)}}}
.
{{{system(t+u=10,10t+u-11n-8=0)}}}


{{{u=10-t}}}
substitute.
{{{10t+(10-t)-11n-8=0}}}
{{{9t-11n+2=0}}}
{{{9t=11n-2}}}
{{{t=(11n-2)/9}}}


Pick to test values of whole number n from 1 to 9 to find which will give
a whole number result for t.


n__________________resulting t
1___________________1
2___________________x
3___________________x
4___________________x
5___________________x
6___________________x
7___________________x
8___________________x
9___________________x


Only n=1 gives a whole value for {{{highlight(t=1)}}}.
With that t, what is u?
{{{u=10-t}}}
{{{u=10-1}}}
{{{highlight(u=9)}}}


Your unknown number is then {{{10*1+9=10+9=highlight(highlight(19))}}}