II want to add two integers with different digits to get a third integer with different digits. At the end, all 10 digits have to be different. So there should be 10 digits in total. How you distribute them is your (or Mathematica's) decision.
Lets say these numbers are $X$, $Y$ and $Z$, so that $X + Y = Z$. There is no rule how many digits a number should have. For example $X$ can have two digits or it can have three digits. What is the maximum possible value for $Z$?
How can I tell Mathematica to chose such two numbers in order to get a third one which satisfies the conditions I impose above? Please explain your answer in simple terms. I am a beginner, and I want to understand the code in the answer so I could do it on my own at some later time.