Imagine connecting these two cells into a circuit, with some other components. Now you'll have charges circulating throughout the circuit; and those same charges move through both cells.

As the charges move through the cells, they gain energy. Each coulomb of charge gains 10J of energy on its way through the 10V cell, and 5J of energy on its way through the 5V cell. Since it gains 15J in total, this is equivalent to having just a single 15V cell.

Those 15J of energy will then be used up by whatever additional components are in the circuit, including the internal resistances of both cells.

Imagine connecting these two cells into a circuit, with some other components. Electrons will move through the wires of the circuit. When the electrons reach the positive terminal of a cell, new electrons with more energy will appear at the negative terminal of the same cell. This happens at both cells.

Each electron entering the 10V cell is replaced in the circuit by an electron with 10eV more energy; and each electron entering the 5V cell is replaced by an electron with 5eV more energy. All these electrons are indistinguishable from one another, except for the energy that they carry. And therefore, the overall effect is equivalent to a single cell where each electron is replaced by an electron with 15eV more energy - that is, a 15V cell.

Those 15eV of energy will then be used up by whatever additional components are in the circuit, including the internal resistances of both cells.