"The old wizard was looking for a wife."
Translation:Den gamle trollkarlen letade efter en fru.
You can use the -e form for essentially any adjective when talking about males. It's virtually the only remnant from when Swedish used to make distinctions between physical gender. However, like Arnauti said, it's entirely optional and quite a lot of people use -a for everything. Either is perfectly fine.
Ah okay, that is handy to know, maybe not for using it myself but certainly for understanding text. Out of interest can it be used in these situations also?
Lärarna är gamle (providing they are all male)
Läraren är gamle
En gamle lärare
Någre lärare (I suspect I'm pushing the concept too far with this one!)
We found one case where it's pretty much standard to use the -e form: old names for kings etc like where the adjective comes last, e.g. Peter den store 'Peter the Great' – this class isn't really productive anymore, but if you wanted to try to create new ones of the same kind anyway, you probably should keep the M/F distinction in the adjective. For the old ones it would certainly sound odd to say Alexander den stora instead of store. Otherwise as devalanteriel said.
You're even missing a "the", since all three are in the definite:
den gamla trollkarlen
It's always like this whenever you have an adjective describing a noun - you then also need an article, and all three need to be either definite or indefinite. (Possessive pronouns work a bit differently.)
But I wouldn't think of it as "the the old the wizard". Linguistics textbooks would usually write it as e.g. "the old-the wizard-the" to make the point that the definites are just markers on the words.