Efficient is defined as performing or functioning in the best possible manner with the least waste of time and effort; having and using requisite knowledge, skill, and industry; competent; capable. The most important aspect of this definition is time. If something is efficient it means does not waste time or energy implying that more can be done.
Example: I finished my homework without taking unnecessary study breaks.
I finished my homework efficiently.
Effective on the other hand, means adequate to accomplish a purpose; producing the intended or expected result. This means something works at meeting the goal it was used for it does not imply a timeframe or give the reader any clue of how much energy was used to complete the task.
Example: The analgesic gave me relief from my headache.
The analgesic was effective.
So they are not mutually exclusive something can be efficient but not effective at remediating the problem or in the inverse something can be effective at producing an desired outcome but not efficient.
I hope that helped.