Some possibilities that just cross my mind:
The most likely cause would be a somewhat older engine on one side with a worn out or just dirty compressor and well broiled turbine blades.
A rather inconvenient cause would be ruptured pressure pipe between the HP pump and the nozzles for example. This would increase the fuel flow for a defined N1/Torque/EPR (or whatever the engine performance is measured by) while leaving the exhaust gas temperature mostly unchanged.
I am sure though that there are other possibilities.