What happened there is maybe similar to what happened to the Eta Carinae system: this
As the second star (which is now a white dwarf) became a red or a blue giant (it may have easily been a star with 10-20 Solar masses), the first star (that is now a white-blue supergiant) accreted material from the second one. What is left from the second star is its core- a white dwarf and a hypergiant star as the first one.
The only way this system is possible is to have the planet in the exact center of mass of the system.
Then, assuming the supergiant must have 40-50 solar masses and the white dwarf is 1.4 max, then the planet should be approximately 40 times closer to the big star then to the dwarf. Knowing the surface temperatures on the dayside are not like 1000K or more, the distances should be BIG. So the orbital periods should go to hundreds of years.
Maybe the planet's atmosphere is very reflective or absorbing in the UV spectrum, otherwise people on the bright side would be black. People on the dark side have darker skin because the white dwarf usually has a surface temperatures as high as 100000K, which makes it glow almost entirely in UV. Then, the most of the UV light from the bigger star will be absorbed / reflected, which also applies for the dwarf, but it produces hundreds times more UV than a regular star, so it becomes noticeable on the surface, resulting in darker skin and fluorescent glow.
But, there is a problem, the dark side would be REALLY cold if the temperatures on the bright side are not extreme. So there must be some really big air mass movements to distribute heat more evenly across the planet, which may be the Shard's work to make the planet more inhabitable.
Even if this exists, everyone on the bright side will be instantly pierced with Industrial quantities of high-energetic particles, resulting in almost instant death or radioactive poisoning in the matter of seconds. The only solution to this problem is a VERY STRONG magnetic field, wrapping the planet, which can be created in two ways
1. Fast spinning molten metal core of the planet (like on Earth, but bigger and faster spinning), which is not possible, because Taldain is practically not spinning.
2. Magic
Well, thats all from me. Have a great day!