How to get the difference between two currents by using only analogue circuitry?
An instrumentation operational amplifier (IOA) can be used to measure the voltage difference between two nodes, in this case, the voltage drop across a shunt resistor. Assuming that you have a positive and a negative voltage rail, the "positive and negative" current can then be worked out by diving the output voltage by the IOA's gain and then by the shunt resistance.

NOTE: The following circuit would not be applicable for measuring "negative" current.
$$V_{out} = (1+\dfrac{2R_1}{R_{gain}})\dfrac{R_3}{R_2}(V_2 - V_1)$$


Source

Here is a working example. As you can see, the calaculated current has a very correlation with the actual current flowing through the shunt resistor \$R_1\$. The IOA gain is set to \$3\dfrac{V}{V}\$ and the shunt resistor equals \$10m\Omega\$.