Find the area of the region enclosed by the graphs of the functions \[ f(x)=18 e^{x}, g(x)=-x+18 \] and the line \[ L: x=18 \] by partitioning the $x$-axis. (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Step 1 ：First, we need to find the intersection points of the two functions $f(x)=18 e^{x}$ and $g(x)=-x+18$. We set $f(x) = g(x)$ and solve for $x$.

Step 2 ：We have $18 e^{x} = -x + 18$. This equation is transcendental and cannot be solved exactly. However, we can approximate the solution using numerical methods. For the purpose of this problem, we will assume that the intersection point is $x = a$.

Step 3 ：Next, we need to find the area of the region enclosed by the two functions and the line $x = 18$. This region can be divided into two parts: the region to the left of $x = a$ and the region to the right of $x = a$.

Step 4 ：For the region to the left of $x = a$, the function $f(x)$ is above $g(x)$. The area of this region is given by the integral of the difference of the two functions from $x = 0$ to $x = a$, which is $\int_{0}^{a} (f(x) - g(x)) dx = \int_{0}^{a} (18 e^{x} - (-x + 18)) dx$.

Step 5 ：For the region to the right of $x = a$, the function $g(x)$ is above $f(x)$. The area of this region is given by the integral of the difference of the two functions from $x = a$ to $x = 18$, which is $\int_{a}^{18} (g(x) - f(x)) dx = \int_{a}^{18} ((-x + 18) - 18 e^{x}) dx$.

Step 6 ：Adding these two areas together, we get the total area of the region enclosed by the two functions and the line $x = 18$, which is $\int_{0}^{a} (18 e^{x} + x - 18) dx + \int_{a}^{18} (-x + 18 - 18 e^{x}) dx$.

Step 7 ：Finally, we can evaluate these integrals to find the exact area of the region. The final result should be in the simplest form.