Lots of you sent in particular numbers that you spotted.

Kristian noticed that $19$ works:

$1+9=10$
$1 \times 9=9$
$10+9=19$

Daniel found that $29$ works:

$(2+9)+(2 \times 9) = 11+18=29$

Bill and Ben discovered that $39$ works:

Because $3 + 9 = 12$ and $3 \times 9 = 27$ and $27 + 12 = 39$

Class 5AA at Raglan Junior sent us something interesting:

Any two digit number which ends in $9$ will give you the solution. However you can't use $99$ as the digits are the same.

But why does this work? Daniel, from Bacons College, sent us his explanation:

The $2$ digit number has $a$ tens and $b$ units, so I can write the equation for this question like this:

$a + b + a \times b = 10 \times a + b$
so: $a + a \times b = 10 \times a$
so: $ a \times (1 + b) = 10 \times a$
so: $b = 9$
and it turns out that $a$ can be anything!

I think that what Daniel means is that a can be any of $1, 2, 3, 4, 5, 6, 7, 8,$ because it can't be $9$ (as Class 5AA pointed out, $99$ isn't allowed). But the idea of using algebra is a good one, if you've met it. Otherwise, you could just try all $8$ numbers.