Because your nut job equation makes it possible for you to need the 4th power of a negative number..
This is like talking to a fence post. By now it should have dawned on you how idiotic it is to calculate P for a negative T difference and get a negative P....which in turn can not be resolved for T.
You had to check your own calculator to see if it can?.....Hahaha anybody with just a minimal math ed would have known that it can`t.
Isn`t it funny though how this guy is deluding himself that his refusal to acknowledge the stupidity of his negative power concept is preventing anyone from seeing right through his lame attempts to grand stand as some sort of science guy. He would have no idea how to solve any real world heat exchange problem unless its been an example posted on some sort of physics for dummies web site.
People like Wuwei and his

clickers are of no consequence and leave no legacy beyond their digital chicken tracks on the internet. While I had to come up with real solutions for real (engineering) problems that better were 100% correct or else....,.to make a living these kind of people lived of my taxes which paid for the dope they use to "chill out".
Why would you ever want to take the fourth root of this equation
P
net =
e sigma A(T⁴ - Tc⁴)
You can take the fourth root of this equation to get emission temperature
P =
e sigma A T⁴
You get total nonsense if you take the fourth root of this equation which is the power absorbed.
P
c =
e sigma A T
c⁴
That is because the SB law refers to emission NOT absorption. Yes it will give you something in units of temperature, but that "temperature" is meaningless. The "Power absorbed" could be identical with a warm source up close compared to a very hot source further away.
You get even more nonsense if you take the fourth root of this equation even if T > Tc.
P
net =
e sigma A(T⁴ - Tc⁴)
The idea of the fourth root is to get the emission power from a known temperature. This equation will not give you anything that is meaningful.
If you think the fourth root of equations that include absorption means something, tell me what you think it is.