1. **State the problem:** Solve for $y$ in the equation $$\ln(y - 3) = 2t + t^2.$$\n\n2. **Recall the formula and rules:** The natural logarithm function $\ln(x)$ is the inverse of the exponential function $e^x$. To solve for $y$, we exponentiate both sides to undo the logarithm: $$y - 3 = e^{2t + t^2}.$$\n\n3. **Isolate $y$:** Add 3 to both sides: $$y = 3 + e^{2t + t^2}.$$\n\n4. **Check domain:** Since $y - 3$ must be positive for the logarithm to be defined, and $e^{2t + t^2} > 0$ for all real $t$, the solution is valid for all real $t$.\n\n**Final answer:** $$\boxed{y = 3 + e^{2t + t^2}}.$$