Is there a way to get a closed form of the radiative cooling equation which allows me to solve for temperature at a given time (T(t) = something), given a set of initial conditions. Here is the hyperphysics page describing radiative cooling:

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html

I followed the same logic as the Newton Cooling equations and ended up with a horrendous mess.

https://www.wolframalpha.com/input/?i=DSolve%5By%27%28T%29%3D%3D1%2F%28T%5E4-a%5E4%29%5D

I know this can be simplified further by putting arctan in terms of natural logs but that still doesn't really get me anywhere. I end up with exp^(time) on one side and several terms that depend on T on the other, but with complex exponentials that make a mess of everything.

Anyways, just wondering if there is a nice equation for this or not, and if so, where could I find it? Thanks