= Solution
For <background-subtracted radiative temperature uncertainty>, assume the two quoted precisions are independent <standard uncertainties>, and treat the radiative proportionality factor as known. Write $P_B=B$ and $P_T=10B$. Then $P_S=9B$, while both absolute input uncertainties equal $0.5B$. Consequently
$$
\sigma_S=\sqrt{(0.05\times10B)^2+(0.50B)^2}=\frac{B}{\sqrt2},\qquad
\frac{\sigma_T}{T}=\frac14\frac{\sigma_S}{P_S}.
$$
Thus \b[the <temperature> precision is about $1.96\%$, or $2\%$]. Subtraction amplifies fractional uncertainty even though $P_T$ itself is precise.
Independence is a measurement assumption, not a consequence of the two percentages. For <correlation> coefficient $r_c$, the result is $\sigma_T/T=\sqrt{2(1-r_c)}/72$. If the percentages are strict error bounds combined pessimistically, the corresponding bound is $2.78\%$. Unknown calibration <correlations> cannot be inferred from the source.
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