I recently finished the book Applied Minds by Guru Madhavan. When I first decided to read it, my wife Rachel asked me "Why do you need to read that?" My response was "Maybe I want to learn why I think the way I do!"
The reality is that engineers do approach the world in a different way. While scientists and engineers tend to get lumped together (see "STEM" for example), even those two professions approach the world in very different ways. As Madhavan points out in his book, scientists largely focus on experimentation and a reasoned approach to a problem. Engineers tend to focus on systematic thinking - analyzing all of the different influencing components in a problem and moving to implement a solution that incorporates the variables into a solution (now whether it is the best solution, can always be left open to discussion).
By looking at some of the classic engineering solutions including the UPC code, the mass production of penicillin and the design of the seat belt, the book shows how engineers approach a problem and look for a solution.
The reality is that - whether I was conscious of it or not - that ability to look at a problem and consider everything around it when coming up with a solution, is what I have always loved about engineering. Whether it is ride control in the theme park industry or process control, systems engineering has always been a source of endless fascination (and that's why I chose it as my major in college).
One example is one of my favorite companies in the world - the design firm IDEO. They worked on a project for Courtyard by Marriott to design a new lobby. At first glance, a hotel lobby may not seem like a big engineering challenge. However, Courtyards are primarily business hotels. Business travelers have different needs than vacation travelers. By conducting detailed ethnographic research - looking at how business travelers use their surroundings, what works, what doesn't work - IDEO and Marriott were able to redesign the entire Courtyard experience to better cater to the needs of the primary user.
Engineering challenges come in a variety of different flavors. But the one thing they have in common is the fundamental approach. By approaching the problem with a view of the entire system at work, engineers bring their own skills to the table and a novel solution is never far behind.