Проблема is something that is not good, 'a trouble'. Задача is something to be done, 'a task'.
Both can be translated as 'problem' in English, but in Russian they are very different things.
I think it's closer to 'task' (or 'problem' when it doesn't have a negative meaning).
'Challenge' is pretty hard to translate in Russian, we just don't have a concept that is similar enough. I tend to translate 'challenge' as «сложная, но интересная задача» ('difficult, but interesting task'), although in most cases I try to re-word sentences using 'challenge' so that they don't use this concept.