Golding shows us mankind's dark side. But why doesn't he present a solution?

Yes - it's interesting isn't it. luannw has given you a good overview on Golding's theory of the "blackness within", and the "darkness of man's heart". But I think there's also a political dimension to this question:

Here's a quote from William Golding:

The theme (of Lord of the Flies) is an attempt to trace the defects of society back to the defects of human nature. The moral is that the shape of society must depend on the ethical nature of the individual and not on any political system however apparently logical or respectable.

The argument Golding is making that it is a society full of good individuals that becomes a good society. That you can't impose goodness through rules. You have to foster it from within. And the society in which "Lord of the Flies" is located is set in a war - the plane is "shot down", and at the end, its a naval officer who rescues. The sort of behaviour in the book, Golding argues, is what a society at war breeds.

So the structures of the civilisation in which the novel is set are at fault. And within that, the boys' behaviour - being seduced by the glamour of a mask, a hunt, and persecution of others, particularly with a tyrannous leader like Jack - is strongly reminiscient of the behaviour of many countries during World War II and the rise of Nazism. Our structures, Golding argues, are clearly not trouble-proof, clearly not darkness-proof.

But more interestingly, Golding seems to be arguing that any structure (however apparently logical or respectable) is wrong, is a bad thing. Society should depend on the ethics of an individual, not on a group policy or ideology.

So maybe that is the solution. Individuals forming societies based on their own ethics. It's a complicated one: wouldn't that be an anarchy - everyone doing their own thing? Where does a sadist like Roger fit into that? What about the vulnerable members of society (the littluns)?

But that, I think, is what Golding is arguing.