That's a rather badly non-linear equation. Typically such equations do NOT have what you call an "algebraic" solution. A better question would be a 'why should it have such a solution?"
sorry to be persistent.. I just want to make sure I understand exactly
so how could you tell straight away that it couldnt be solved? is there a name for such equations? what characteristics make it such that it cant be solved?
many thanks - much appreciated