Calculate the value of $T,$ to the nearest $0\mathrm{.}1K,$ for the following integral equation. Note that $7\mathrm{.}666E-5$ is equivalent to $7\mathrm{.}666{10}^{-5}.$ Hint: Use a solver function in Excel or on your calculator.

$15,000\frac{J}{m}ol={\displaystyle \underset{298}{\overset{T}{}}}[27\mathrm{.}44+0\mathrm{.}08127T-(7\mathrm{.}666E-5)T^2+(2\mathrm{.}673E-8)T^3]dT$