The battery light tells you that the battery is not being charged - eventually it will go flat.
Engine management light is another matter - that tells you that there may be something wrong with the engine people say on here that the engine management computer needs to be checked to determine the reason for the light. They say a code reader should be attached.
The car may have bee checked but I suspect it's far from fine - two warning lights are permanently on.
You need to make a small investment...
Good luck...
N Mansell, September 2014