Overview

Believe me, I have wasted hours on this problem. You will probably be best off using Anaconda. You can find all the details here: TF installation guide
Keras itself should already be packed inside Anaconda, if not use (source: here):
conda install -c conda-forge keras=1.0.7

But.. If you do not want to install Anaconda, for whatever reason, this is a guide for you!

Install pywin

What it is - sourceforge project site: Pywin
Get a suitable version from here (for your python version and Windows version): Builds

Follow installation instructions. After it finishes, basically in that folder you have a separate python interpreter with already installed various libraries for calculations! You can update libraries using:

<path to pywin>\python.exe -m pip install --upgrade keras

Install tensorflow

<path to pywin>\python.exe -m pip install tensorflow-gpu

Check installation.

Run your favourite IDE and try these imports:

import keras
import tensorflow
import scipy
import numpy
import pandas

Try a simple project!

Here - this one should work!
Simple Neural Net with Keras + TF