Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
There is no contradiction between the texts, because the Day of Resurrection is long and contains multiple stages, situations, and conditions. Therefore, it is not necessary for all the events mentioned concerning that Day to occur at the same time.
It has been reported that the sun will draw near to the creatures in the gathering place, causing the heat and distress upon them to become severe. This is established in the hadith of the Great Intercession recorded in the two Sahihs.
It has also been reported that the sun and the moon will be rolled up on the Day of Resurrection. Allah تعالى says:
﴿إِذَا الشَّمْسُ كُوِّرَتْ﴾
“When the sun is wrapped up.”
And it is mentioned in the hadith:
“The sun and the moon will be rolled up on the Day of Resurrection.”
According to the view that the rolling up mentioned in the verse is the same event referred to in the hadith, then the sun’s drawing near to the people would occur at one stage of the Day of Resurrection, followed afterward by its being rolled up and cast away. Thus, there is no need to say that there is another sun.
Some scholars have held that Allah’s statement:
﴿إِذَا الشَّمْسُ كُوِّرَتْ﴾
refers to events that occur immediately before the establishment of the Hour, when the order of the universe is disrupted. In that case, the rolling up of the sun would occur before the Day of Resurrection, and then, after the Resurrection begins, the sun would draw near to the creatures. According to this interpretation, the apparent difficulty disappears altogether.
Most importantly, the conditions of the sun on the Day of Resurrection are multiple, and they cannot be compared to its condition in this worldly life, because that Day has a system and conditions different from those of our world.
In conclusion: there is no need to say that there is a second sun. Rather, the texts can be reconciled by saying that the sun’s drawing near and its being rolled up occur at different stages, or that the rolling up mentioned in Surat At-Takwir occurs before the establishment of the Resurrection, depending on the difference among scholars in interpreting the verse.
And Allah تعالى knows best.