How to calculate blackbody temperature from radiance band?

[eng3]

I know how to calculate blackbody radiance in a spectral band from a temperature by integrating (or summing) planks function.

How can I do the reverse? For example, I have a Radiance of 1000 W/m^2/sr in the 3-5um band, I'd like to be able to calculate 666.6K.

 

[drvrm]

T=hc/{L*k *{ln{2h*c^2/(L^5*R)}+1}}
the above formula is quoted in the reference given below;
L is wavelength ,k is Boltzmann constant, h and c are usual well known constant R is radiance...well i do not know details you have to search.

ref.-http://oceancolor.gsfc.nasa.gov/forum/oceancolor/topic_show.pl?tid=5478

off course the peak value of wavelength is also related with temp.

 

[eng3]

I did see that, and that gives the temperature for one wavelength.

My radiance is over a band.
For example, in a BB calculator, I can put in 666.6K, over the 3-5um band, and it will give me 1000 W/m^2/sr
How do I do the reverse? I have 1000 W/m^2/sr in the 3-5um and I want to calculate the temperature