Perhaps I can answer it like this.
Firstly the actual physical world measured solar insolation is 1,361 W/m^2 , which is equivalent to a blackbody temperature of 120.46C , not -18C.
How do they get from 120C to -18C? This is done by a trick of mathematics. They observe that the Earth receives this 1,361 W/m^2 across a circular cross-section – the intersection of the Sun’s emitting sphere of rays, with the Earth’s spherical surface. Then they assume that by some definition of ‘equilibrium’ the Earth must be emitting this 1,361 W/m^2 at all times, evenly, across its entire surface area, which is 4 times the surface area of this circular cross-section that it receives from the Sun. Therefore the Earth emits 340 W/m^2 at all spots. They then further apply the “energy out = energy in” yet again to say that the Sun just provides 340 W/m^2 at all times – even though it’s really 1,361 W/m^2! You can see this in the energy budget diagrams.
Then even though this is supposed to be a calculation of an atmosphereless Earth, they still take the albedo of 0.3 into account, which is due to clouds and such, therefore this 340 is multiplied by 0.7 to result in 238 W/m^2, which is equivalent to a blackbody of -18C .
The entire premise here is that energy in equals energy out at all times instantaneously across the entire Earth. This mathematically reduces the Earth to a flat disk that’s twice as far from the Sun and has 2x the radius as the actual Earth, with equal amount of light impinging upon each square millimeter that’s equally radiated out at all times etc. This is what the -18C is.
Therefore, by their very model, they are saying the Sun is equivalent to basically being in a vast flat room with a -18C ceiling way ‘up there’ and with a -18C floor.
After all these transmogrifications, it doesn’t make sense to say the Sun of 5500C is “really” the heat source – because they’ve already mathematically manipulated this physically real 5500C heat source, into a -18C one.
Then they do the further magic math to eke out +15C out of this reduced-to-negative-18-C heat source, i.e. the physically impossible thermodynamic violation.
One could argue that in reality the sun really is hotter etc., but by then you’re already departing from the model that is the premise of the whole thing. The model must be addressed in terms of the model. You will observe in arguing with warmists that they change the goal posts to suit them based on what they’re arguing. When measuring the magnitude of the effect, it doubles or triples the amount of Sun coming in! And it’s all possible cause the Sun is much hotter anyway! Yet in the model that calculates this doubling or tripling, the Sun isn’t! The model doesn’t account for the real temperature of the Sun. It reduces it to this cold -18C.
Perhaps that answers the question?
Cheers,
Claudiu