Edward Elric can't get back to his own world, so he tries to make a life for himself in the closest one he can find. Yep a nice quiet life, no military breathing down his neck or monsters trying to live forever, but then a kid in an orange jumpsuit...
Following Al's restoration, the Truth sends the Elric Brothers to another universe with zero information. Neatly forged paperwork lands Ed a job teaching summer school remedial chemistry to children who are older than he is. Due perhaps to cosmic ineffability one of these summer school kids can lead the Elric brothers to precisely who the Truth had in mind. Book 6, Brotherhood.
Albus Dumbledore needs an Alchemy teacher. Roy Mustang needs a spy. Edith Elric needs an adventure. They help (use) each other. (Or, alternatively: Ed goes to teach at Hogwarts. Britain doesn't know what hits it.) Female!Edward
When the alchemy of Amestris proves insufficient to restore their bodies, the Elric brothers turn to knowledge of another world. Truth's toll is uncharacteristically forgiving, but perhaps Remnant's ills will be their payment to come. Nonetheless, if their quest requires dealing with yet another shadowy organisation intent on surpassing the domain of humanity, then so be it.
When Roy Mustang went to retrieve his eyesight from Truth, he wasn't expecting to end up doing a job in exchange. It couldn't even be an easy job, of course, because Edward's assessment of Truth was a pretty accurate one.