1. **State the problem:** Solve the equation $9e+4 = -5e+14 + 13e$ for $e$. 2. **Rewrite the equation:** The equation is $9e + 4 = -5e + 14 + 13e$. 3. **Combine like terms on the right side:** $-5e + 13e = 8e$, so the equation becomes $9e + 4 = 8e + 14$. 4. **Isolate the variable $e$:** Subtract $8e$ from both sides: $9e - 8e + 4 = 14$ which simplifies to $e + 4 = 14$. 5. **Solve for $e$:** Subtract 4 from both sides: $e = 14 - 4 = 10$. **Final answer:** $e = 10$