VoltageAdder

Circuit:

Analysis:

The negative feedback by the Opamp will drive the negative input of the Opamp to be zero.

The current from the power sources cannot enter the Opamp because Opamp has high input impedance, it will flow the $V_{out}$.

The total current is:

$\frac{V_1}{1} + \frac{V_2}{1} = \frac{0 - V_{out}}{1}$.

Simplifying, getting $V_{out} = -(V_1 + V_2)$

Simulation:

To show the addition, I used two different sine waves with different frequencies and amplitude for $V_1$ (green) and $V_2$ (blue). The negative sum is shown in below.

LTSpice:

The model can be downloaded here.