Let's first rewrite the equation you have provided for clarity.

From your equation:

\[
(X+1) + (X+2) + (X+3) + \ldots + (X+18) = 207
\]

To simplify, we'll express the left-hand side. Notice that we can combine the terms as follows:

\[
(X + 1 + X + 2 + X + 3 + \ldots + X + 18) = 18X + (1 + 2 + 3 + \ldots + 18)
\]

We know that the sum of the first \( n \) integers can be computed using the formula:

\[
\frac{n(n + 1)}{2}
\]

For \( n = 18 \):

\[
1 + 2 + 3 + \ldots + 18 = \frac{18 \cdot (18 + 1)}{2} = \frac{18 \cdot 19}{2} = 171
\]

Substituting this back into our equation gives:

\[
18X + 171 = 207
\]

Now, let's solve for \( X \):

\[
18X = 207 - 171
\]
\[
18X = 36
\]
\[
X = \frac{36}{18} = 2
\]

Thus, the solution to the equation is:

\[
X = 2
\]