Vaermina quest in skyrim

Solution 1:

Yes and no. If you are trying for the Oblivion Walker achievement you will need to collect the skull of corruption (or take advantage of a bug in another quest).

If you just want one to play around while saving Erandur, you can just use a console command if you are on the PC to give yourself one:

player.additem 35066 1

Solution 2:

You can only get one or the other. I killed Erandur and got the skull on my latest playthrough so that I could get the oblivion walker achievement, but if you don't want the achievement I would advise sparing Erandur because the skull of corruption is a trash weapon anyway, it has 20 base damage (which can be increased to 50, but if you have good one handed, two handed or destruction that's still not great).