Difference between Engineering and Re-engineering

Can you please explain the difference between Engineering and Re-engineering? How both are related to each other what are their individual purposes.

Engineering is a path going from a problem to solution. Problem is identified, solution is proposed, developed and delivered. This is engineering. Now system is in use. After sometime, we want to update due to any business requirement then we will re-engineer it. Reengineering is the modification of a software system that takes place to add new functionality, or to correct errors.Re-engineering' is a set of activities that are carried out to re-structure a legacy system to a new system with better functionality and conform to the hardware and software quality constraint.Purpose of engineering is to solve some real life problem where purpose of re-engineering is to reconstitute it in a new form to make it better.