I don't really understand what your question means but... I'll try to answer it.
Soo I believe that number is 18k
After the addition, it's 18k+10
Since that is divisible by 10 (I think that was what you meant), that means 18k is divisible by 10
Since \(18=2\cdot3^2\), \(10=2\cdot5\), that means the k must be a multiple of 5.
So to keep the number a 2 digit number, k must be 5
Therefore the number Anna chose was 90
Sorry if this didn't help, because I don't really understand your question.

Oh, sorry, I mixed up the divisor and the dividend 
Okay, so that number is divisible by both 18 and 28.
\(18=2\cdot3^2\)
\(28=2^2\cdot7\)
The least common multiple of these two numbers is... that's 3 digits...

18k is divisible by 28, is that what you mean?
That means 9k is divisible by 14, which means k is at least 14 and...
That's still 3 digits...

So what if it's 18k+10 being divisible by 28, adding 10 to both the divisor and the dividend.
So.... k can only be 1, which means the number Anna chose is 18?

Please, next time, have proper grammar in your sentences for us to understand  The question should've been:
"Anna chose a 2 digit number. That number is divisible by 28. If you add 10 to the divisor and the dividend, the new dividend is still divisible by the new divisor. What number did Anna choose?"

hey Ton That Khac Trinh, you are wrong . 90  cannot divisable 28.