Restore whole system on 10.10 with time machine

So,

i realized that I somehow destroyed some very important files on my computer. I am working with QGIS and I deleted in my pythons system native folder some egg's and so forth which led to the inconvenient outcome that my QGis is not working anymore...

Luckily, I have a backup from yesterday night.

My question: Can I restore my whole system from that backup? Basically, I want a clean set up with 10.10 and then, all my installed C++ compilers, libraries for Python, plug ins and so forth back on it again.. Is that possible? If so, how?