$\text{ Let }\mathrm{E}\text{ and }\mathrm{M}\text{ be }3\times 3\text{ matrices satisfying the system of equations }{\mathrm{EM}}^{\mathrm{T}}=(\mathrm{EM}{)}^{\mathrm{T}}=20 I. \text{ and }(\mathrm{E}+\mathrm{M}{)}^{\mathrm{T}}=17(\mathrm{E}-\mathrm{M}{)}^{\mathrm{T}}$

$\text{ where I denotes identity matrix of order }3.$

$\text{ If }{\mathrm{E}}^2+{\mathrm{M}}^2=\frac{\mathrm{a}}{\mathrm{b}}\mathrm{I}\text{ (where a and }\mathrm{b}\text{ are co-prime), then the value of }(\mathrm{a}+\mathrm{b})\text{ is }$