Hey! what could be the problem if the engine light is on and sometimes even the battery light comes up

I took my X type jaguar for routine service, and when it came back 2 weeks later the
engine light started to be on and sometimes the battery light also goes on but i took it to
battery center where they confirmed the battery is okay, but now i am more worried about
the engine light that is always on and getting afraid it might cause damage to other parts
or the engine itself, what can be the problem and how can it be fixed?