Math gurus - Multiple Unknowns = Result Quadradics?

Hi all, not sure if I can phrase the post better so please bear with me.

I have a set of accounts and a premium from 08-09. In the accounts will be all the activity. The premium (insurance) lists things grouped together such as vehicle insurance, Material damage. They have grouped all the sub headings together and given me a total for each.

So I have the sum amounts written on the premium to hand and the individual (breakdown) amounts in the accounts. I need to find the amounts that add up to the premium sum and although I managed to find a few from cherry picking, I'm now lost.

As usual, it's 'report on my desk by Monday' so beside scratching my head and continuing to cherry pick, I hoped one of the masters on here might know a little mathe-magic that could help? I thought about quadratics and simultaneous equations but there could be anything from 2 fields to 20.

Help!