I subtract 9 from your answer, and the digits of the number that I'm left with, are your two numbers.
For example, if your final answer is 74, when I subtract 9, I get 65, so I know your numbers were 6 and 5.
How does it work?
If the two numbers are $a$ and $b$,
|Take one of your numbers||
|Multiply by $5$||
$5(a+1) = 5a+5$
|Add $1$ again||
$5a+5+1 = 5a+6$
|Double your answer||
$2(5a+6) = 10a+12$
$10a+12-1 = 10a+11$
|Add your second number||
$10a + 11 + b$
$10a + 11 + b + 2 = 10a + b + 13$
$2(10a + b + 13) = 20a + 2b + 26$
$20a + 2b + 26 - 9 = 20a + 2b + 18$
|Halve this number||
$\frac12(20a + 2b + 18) = 10a + b + 9$
Final answer is $10a + b + 9$, so I subtract $9$ to leave $10a+b$
$10a + b$ is $a$ tens and $b$ ones
Since $a$ and $b$ are both less than $10$, they fit in the tens and ones columns and so they are the digits of the number.