I'm not a controller although i think if you call that you have an engine failure, then its reasonable to assume that you will be busy. If you haven't declared a Mayday, then may ask the pilot and just get everything out of the way to assist the aircraft with an engine failure. I believe its recognised that the make of the aeroplane is known and that only one engine has failed for a 737 for example, an emergency is declared regardless since the aeroplane has lost 50% of its power supply. I think this is the general rule.
At the end of the day, the controller will be aware that you will be very busy and just try and get everything out of your way but he will need to know some details of the emergency to alert the appropriate services on the ground i would assume.
hope this helps