1) "solves for" means you DO want it to be exact. More precise language is always helpful.

2) You must formulate some sort of model. Where do the data come from? What sort of model might be appropriate? Are there ANY known relationships? How sure are you that all your variables are independent? Are there linear relationships or are they ALL nonlinear? A scatter plot of 'a' vs 'b' might suggest a linear relationship.

3) Are there any dependencies inside a single variable?

4) Excel does just fine with Multiple-LINEAR Regression. It's in the Data Analysis Tool Pack. p-values and everything.

5) Sometimes, you can make non-linear relationships linear by applying a logarithm or square root transformation. There are other sorts of transformations. Can you see any opportunities for transformations?

6) What sort of nonlinear relationships are you anticipating or imagining? Just polynomials of order higher than one (1)? Reciprocals? Rational Functions? Trig Functions? Logistics?

7) Ever hear of "R"? You can pursue any sort of GLM with enough R experience.

https://www.r-project.org/about.html To be honest, you'll probably need more data to get very far.

8) Is this a student problem, a personal exploration, or maybe a business requirement? Purpose and audience are just as important as methods.

We're happy to help, but you have to show your work and give us something to go on. We all have opinions on how one might proceed, but if we are going to get YOUR views that lead to YOUR personal solution, you will have to offer up quite a bit more information.

Direction please.