Let $a$ and $b$ be real numbers. For functions $f$ and $g$ defined on the set of real numbers
$$\begin{aligned}
& f(x) = x^{2} + ax + b \\
& g(x) = ax + 2 \\
& (f + g)(3) = 4 \\
& (f - g)(5) = 6
\end{aligned}$$
These equalities are satisfied.
Accordingly, what is the difference $\mathrm{a} - \mathrm{b}$?
A) 17
B) $\frac{52}{3}$
C) 18
D) $\frac{56}{3}$
E) 19