The examples in my dictionary suggest noe = something while noen = someone.
Two of these examples may help you to remember the difference: ikke noe = not any(thing); ikke noen = not any(one).
This isn't the full story with noe and noen as there does seem to be a little variation in use that challenges the above, but this is a good place to start.
The way I tend to remember it is that 'noe' relates to something uncountable, 'noen' to something that (although you might not know how many) is finite. So, for example, if you are looking for someone (a finite entity, a person, an definite object, something knowable) it is 'noen'; if it is for something undisclosed (an indefinite object) to the person asking, it is 'noe'.