total energy and apparent bolometric magnitude
You have been given a terrible question and your confusion is totally justified.

The magnitude system is a measure of the brightness of objects which is a measure of the energy received per unit time interval.

Without knowing a characteristic timescale over which the energy is released in each case, then it is not answerable. Note that the timescale for energy release in the case of supernovae and bombs are different by many orders of magnitude - a type Ia supernova has a bolometric light curve (e.g. see Fig.6 of Scalzo et al. 2014) that lasts 2-3 weeks, peaking at around $10^{36}$ Watts.

Given this, we can compare with the Sun's bolometric luminosity of $3.8\times 10^{26}$ Watts and apparent bolometric magnitude of -26.8, to estimate that the peak apparent bolometric magnitude of a type Ia supernova at the distance of the Sun would be -50.3.

You cannot do the same thing with nuclear explosions. They last a fraction of a second (in terms of their light output). Or are you meant to assume that you take the average flux over the 70 years that mankind has had nuclear weapons?? The question is a nonsense unless you are given some sort of timescale over which this explosive energy is released. About the only sane things you can do are (a) use ~70 years (actually, most of the energy was released during the 1950s and early 1960s) (b) use the duration of a single nuclear explosion or (c) (and I imagine what was intended) use a similar duration as for a typical type Ia supernovae so that the question should have begun - "Imagine that X and Y amounts of total energy are emitted over a similar timescale..."