Do an Op-amps supply pins need to have the exact same nominal voltage?
If your op-amp can swing within 2.2V of the positive rail and within 1.8V of the negative rail under all possible load conditions, and if the inputs likewise are within the allowable common mode range then there is no problem. 

There is no requirement for balanced voltages. You can use -0.1V and +20V if that works as indicated above (and, of course, if the op-amp can handle a 20.1V supply).