Engineering and designing are much more similar than they are different.
I recently completed a four-year graduate design degree (architecture) after a lifetime of math, physics and not a whip of art or design experience. Here's my take on this issue.
Engineering and design are both fundamentally processes of creation. While both creations must meet one or more objectives, the types of those objectives often differ. Engineers tend to optimize for quantitative objectives and criteria; designers tend to optimize for qualitative objectives and criteria.
I think this difference has two significant consequences:
1. The solution space for designers (or anything with qualitative criteria) is much larger than for engineers.
2. There are many more opportunities for mediocre design than there are for mediocre engineering.
By point 2., I mean that not only is the solution space of design much larger, but there are also many more "attractors" of solutions. In engineering, the attractors have a strong pull and are more recognizable as such. And, because the solution space is more quantifiable, the relations between those solutions are more well understood and comparable.
In design, the attractors are more fuzzy and their locations in the solution space are often unknown. This allows anyone who can find a mediocre design solution (especially those who find "pretty" visual ones) to become a "designer". But good designers must do much more. They must understand the design space enough so that, from any starting point, they can justifiably navigate towards that same design solution.
This involves crossing certain thresholds -- bifurcations -- in which the nature of the design solution changes. Recognizing when to cross these thresholds is, in my opinion, a task perfectly suited for analytical thinkers. You don't need to be able to create visually pleasing designs to find the best design solutions. Visual aesthetics are simply one component of optimizing the already discovered design solution.
So my advice to engineers is this: forget about visuals. Design analytically, question the existence of design components and their relationships. If you cannot justify their existences and relationships, you need to somehow change their nature (bifurcate the design) until you can justify it. Often starting from the bottom-up is the best way to accomplish this.
Once a design solution is in sight, optimizing its visual aesthetics is much easier -- you've already framed its problem so well!
Finally, I must note the three tasks which are essential to the design process: research, experimentation and documentation. Surely these tasks are also vital to engineers, or anyone else involved in processes of creation.
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(PS If anyone would like to talk about how many of the concepts of dynamical systems theory can be used in the design process (and the design itself!), I'd love to hear form you!)