I would like to create a neural network, which, given the training data (e.g. 58, 2) outputs a non-binary number (e.g 100). Perhaps I am not searching for the correct thing, but all the examples I have found have shown classifiers using a sigmoid function (range of 1 to 0). I am looking for something that would output nonbinary numbers.
First of all, sigmoid does not output 0 or 1, it outputs any real number in the range between 0 and 1.
Furthermore, neural networks don't usually output binary values, unless the output layer uses the step function as an activation function (which is rare).
I'm not really sure if you want the neural network to be a classifier or regressor, but it sounds like you want a regressor.
Regression is when you are interested in the value of the output neuron(s) itself. A simple example is if you want the network to predict the sum of two input neurons.
If you want to change the network from a classifier to a regressor you should probably reduce the number of neurons in the output layer to 1, and change the activation function of that neuron from softmax to the identity function ($f(x)=x$; which is the same as no activation function at all).