As their name suggests, devices with differential input can subtract two single-ended (grounded) voltages. The transistor is a simple example where the first input voltage is applied between the base and ground and the second voltage - between the emitter and ground. The differential amplifier, particularly an op-amp, is a more sophisticated example where the first voltage is applied between the non-inverting input and ground... and the second voltage is applied between the inverting input and ground.
Actually, in these configurations, the two input voltages are connected in series and opposite (traveling the input loop). So we can say they are summed in a series manner, according to KVL, by the input loop… and the output voltage appears at the differential input. The conclusion is that the humble loop acts as the simplest series voltage summer.
We can enlarge this idea adding/subtracting more input voltage sources by connecting them in series, in direct/opposite direction - Fig. 1. But a problem appears - only two of them can be grounded; others will be floating (ungrounded).
Fig. 1. Summing voltages in a series manner (according to KVL)
This problem can be solved if, instead of summing voltages in series (according to KVL), we sum currents in parallel (according to KCL); thus all input current sources can be grounded - Fig. 2. So the current summer is nothing else than a humble node. It remains only to convert the input voltages to proportional currents by resistors in series (according to Ohm's law) and we will obtain the parallel resistor summer shown in the @S.s. answer.
Fig. 2. Building a parallel resistor summer (according to KCL and Ohm's law)
So, the general conclusion is:
Addition and subtraction are performed by simple electrical circuits and not by active elements (transistors and op-amps). The role of active elements is only to make the passive summing circuits perfect.
For example, in the op-amp inverting summer, the "feedback resistor" R is just another (fourth) input where the op-amp output voltage is applied with such a polarity so that to zero (compensate) the voltage of the common summing point A; as a result, it becomes a "virtual ground". Thus the input currents depend only on the corresponding input voltages and the inputs are independent of each other (they are separated by the virtual ground).
Fig. 3. Op-amp inverting summer
See also my Wikibooks stories about the series and parallel summer.