Let her.
Trust me when you stop trying to make her stay she'll come back on her own or at least your relationship will improve.
But I left home at 16 so can only draw on my own experience at 18 she's old enough to leave if she wants.. You can't call it running away from home I don't think.
If she has nowhere to go (and I'll bet she'll have a bed for tonight) she'll be back when things calm down.