Talk to a lawyer and ask what "detrimental reliance" means. (Short version: what you just did owing to representation that they had a job for you. Comes with damages.) Let your old company tell you you can't have your job back, don't make that decision for them.
I don't want to make a decision for my current company. They may even let me have it back. I'm on very good terms with my team too and they were in fact, disappointed to see me go. I'd just hate myself to go back with my head hung in shame telling them that 'oh my job didn't work out'...take me back. I had a farewell lunch yesterday. Everyone in my extended team knows I'm leaving. My exit interview is planned for ear…
(I always find it easier to deal with unfortunate or embarrassing situations when I'm reminded that they appear more severe and permanent to me than they actually are.)