Solving two electron integral numerically
The canonical text on quantum chemistry is Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund. Every electronic structure theorist I have ever met keeps a copy of that book within arms reach of his/her desk. 

As for software, I would recommend PySCF. It is an entirely free python library for quantum chemistry with the most critical routines written in C and is an excellent platform to develop on. It's also robust and fast enough to be used for large calculations should you want to scale up. (https://github.com/sunqm/pyscf)

PySCF uses libcint to perform the integrals, and contains a low-level interface to the integral evaluator. An example of how to use these methods to make a df-HF calculation is shown in the docs here: https://sunqm.github.io/pyscf/tutorial.html#molecular-integrals. A complete list of available integral routines from the libcint package is shown here (it's very comprehensive): https://sunqm.github.io/pyscf/gto.html#module-pyscf.gto.moleintor