Iterative numerical methods, such as those found in the chapter on root finding in Numerical Recipes can solve this type of problem.

First edition of Numerical Recipes by Press, Teukolsky, et al.

Numerical Recipes, a series of books on algorithms and numerical analysis coauthored by William Press.

Numerical Recipes web site.

Current electronic edition of Numerical Recipes (limited free page views).

I still pull out my old dusty mathematics books, like "Numerical Recipes," when I'm looking for answers to problems.

More detailed descriptions of these, and other, methods are available, in Numerical Recipes, together with computer code in various languages.

Numerical Recipes in C, Go to Chapter 3 Section 3-3.

Open source, except uses Numerical Recipes.

Chapter 15 in Numerical Recipes describes several methods to solve linear equations and estimate the uncertainty of the resulting values.