1. **State the problem:** We are given the differential equation $$\frac{dy}{dx} = \frac{1}{x + e}$$ for $$x > -e$$, and the curve passes through the point $$(e, 2 + \ln 2)$$. We need to find the equation of the curve. 2. **Recall the formula:** To find the curve, we integrate the derivative: $$y = \int \frac{1}{x + e} \, dx + C$$ 3. **Integrate:** The integral of $$\frac{1}{x + e}$$ is: $$\int \frac{1}{x + e} \, dx = \ln|x + e| + C$$ 4. **Write the general solution:** $$y = \ln|x + e| + C$$ 5. **Use the initial condition:** The curve passes through $$(e, 2 + \ln 2)$$, so substitute $$x = e$$ and $$y = 2 + \ln 2$$: $$2 + \ln 2 = \ln|e + e| + C = \ln(2e) + C$$ 6. **Simplify:** $$\ln(2e) = \ln 2 + \ln e = \ln 2 + 1$$ 7. **Solve for $$C$$:** $$2 + \ln 2 = \ln 2 + 1 + C$$ $$\Rightarrow C = 2 + \ln 2 - \ln 2 - 1 = 1$$ 8. **Write the final equation:** $$\boxed{y = \ln(x + e) + 1}$$ This is the equation of the curve passing through the given point.