The engine, a Rolls-Royce RB211-535E4, was shut down and the pilot made a successful emergency landing on one engine.
The aircraft, with 221 passengers on board, was heading for Arrecife, Lanzarote, when the birds hit the right hand engine, causing a flameout and repeated puffs of black smoke. The pilot declared an emergency and dumped excess fuel before landing at 1030.
All twin-engined aircraft are designed to be able to complete their take-off and climb out on a single engine, and the engines themselves are designed to continue providing some power in all but the most severe birdstrikes. In this instance, aftre ingesting two large birds, the pilot shut the engine down immediately.
See a video of the event at: http://www.youtube.com/watch?v=KGIzNJZOw-c