find all two digit numbers with the property that if i sum the digits and add this sum to the product of the digits, i get the number.
I noticed that every number that ends with $9$ works but i would like to know the reason behind this.
$19 \rightarrow 1+9=10 \rightarrow 10+(9 \times 1)=19$
Also works for $29,39,\ldots,89,99$
Any reason why this works?