Actually, the long ä is pronounced different from the long e but especially Northern German dialects don't make that difference except for cases where it matters:
Er sagte, er läse. (Konjunktiv II instead of the Indikativ lese)
Sie bewährte sich gut. (bewehren is a different verb.)
So, how to find out if people aren't going to help you? A word list? No chance, they are too many to remember – thousands. You only have hints:
- There are no words with -ä, -äl, -än endings, and Bär and Mär are the only words ending in -är. This also applies to compounds so you can settle on e, el, en or er in these cases. They are the majority by far. There are exceptions, of cause, as the infamous Erklärbär.
- äh is a long ä and people will pronounce it soft. Even in Northern Germany. No problem here.
- If you know there's a similar word with a, most likely you just encountered a different form of that word.
- If there's a similar Latin word with a or a French word with ai, it's the origin of the German word. This is e.g. the Käse case.
And don't be discouraged, it's one of the fields German first language speakers make the most mistakes.