Actually, I can not tell the difference between engine and framework. It's just two different names.
What really odd is that game engine is all about client side, it seems like you do not need a server framework, whereas pure socket is enough for it.
But the reality is not like this, at least, there should be some framework like rails or django to ease your server development. Not to see game server is harder than web development in scalability, broadcast and other areas.
There is a commercial solution called smartfox server, and a new open source solution called pomelo framework, I've tried both, pomelo is much better. pomelo.netease.com is its home.