I got a quest from Eydis Fireye in the Fighters Guild Balmora to retrieve a codebook from Sottilde from the Thieves guild, but she won't give it to me and says I have to decide which side I'm going to take. I'm a member of both guilds and I want to stay that way, is there a way around this?

There is a way (that I can't remember) but I will actually try to convince you not to use it.. I did it in my first game and I have regretted it ever since. The game will become too easy when you level up and doing too many quest lines will make you too good too soon.. Are you a fighter or a thief? Do what is better suited for your character and the next time you play, do the other one. You will thank me later. Trust me on that.

I think whats so great about the elderscrolls is the fact that the play can do whatever they want. If the OP wants to get the book, let them.

That being said, theres two things you can do.

• Kill her. (do not just attack her. Successfully taunt her until she attacks you)
  
• Steal the book from her. (Save first! Use a chameleon spell/scroll to up your odds!)

I'd personally recommend the second one. Less concequence. But the choice is up to you.

If you want to avoid the quest in general, head over to another fighter's guild hall and pick up some more quests!