What is the difference between problem and challenge?

The key difference is your attitude towards it, a problem is something that stumble on, and you want to get rid of it, but you are not willing to do so, a challenge, on contrary, is an obstacle that you feel motivated to face, as overcoming it might mean a satisfaction feeling (a feel good feeling to do so)

Simple, a problem is faced with calculated resolutions to obtain result, whereas challenge is faced engaging yourself with diplomacy to accomplish the task.