 Solution

For radiative temperature uncertainty after background subtraction, write $P_{\mathrm{back}}=B$, so $P_{\mathrm{total}}\simeq 10B$ and $P\simeq 9B$. The two absolute uncertainties are both $0.1B$. If they are independent standard uncertainties,If the percentages instead denote absolute error bounds, linear worst-case propagation gives 0.56%. With correlation coefficient $\rho$, the standard-uncertainty result is $\sqrt{2(1-\rho )}/360$; subtraction makes positive common errors partly cancel. The independence convention is therefore an assumption, not information supplied by the percentages.