OIM 2012 Problem 2

A positive integer is called shiny if it can be written as the sum of two not necessarily distinct integers $a$ and $b$ which have the same sum of their digits. For instance, $2012$ is shiny, because $2012 = 2005 + 7$ , and both $2005$ and $7$ have the same sum of their digits. Find all positive integers which are not shiny (the dark integers).