1. **State the problem:** We need to find angle $\angle CAD$ in the circle where $AD$ is the diameter, given $\angle ACE = 36^\circ$ and $\angle ABC = 118^\circ$. 2. **Recall the key fact:** In a circle, the angle subtended by a diameter at the circumference is a right angle. So, $\angle CDA = 90^\circ$ because $AD$ is the diameter. 3. **Use the given angle:** We know $\angle ACE = 36^\circ$. 4. **Find $\angle CDA$ using the triangle $CDA$:** Since $\angle CDA$ is right angle, and $\angle ACE = 36^\circ$ is an angle in the same segment, the angle $\angle CAD$ can be found by subtracting $\angle ACE$ from $90^\circ$: $$\angle CAD = 90^\circ - \angle ACE = 90^\circ - 36^\circ = 54^\circ$$ 5. **Explain the reasoning:** Because $AD$ is a diameter, $\angle CDA$ is $90^\circ$. The triangle $CDA$ has angles summing to $180^\circ$, so $\angle CAD = 54^\circ$. **Final answer:** $$\boxed{54^\circ}$$