Approximation search source reconstruction localization algorithm
Remove empty lines after if/else. Remove empty lines in general, this has too many. Use the new math.dist. Add comments about how the approximation works. Add docstrings.
If you want to make it more readable, pull out sub-loops into functions. That reduces nesting depth, which is just too high here--it's a problem you don't run into often. Also, don't use names like 'ei'.
One approach to make it more readable (but maybe slower), rewrite 'approximate' as a function taking in: a function to compute, an interval to search, and a maximum number of iterations. Also, you could use scipy or another specialized package which has this built-in.
If you want to make it more readable AND fast, don't use this solution. Use some other maximization method, for example gradient descent. These are also available as prebuilt tools, so it should be readable.
Last, in this case, I think there is probably a very direct answer specific to the problem. Look up GPS algorithms, because this is more or less how they work (although the speed is always the speed of light)