There's an art to engineering design, though it's not exactly lacking the numerical calculations either. Anyhow, the impression most people have of science-related subjects is what they learn in school; specifically, school up to and through high school. Throughout all of this, you are rarely (if ever) exposed to design. For most of my engineering degree, I didn't even touch or consider design.
If you haven't clued in yet, here's what I'm getting at:
Design changes everything.
Design is a huge leap from mere analysis, and this is what most people see in the sciences in general. And let's be honest, there's nothing all that artistic about analysis; you're just looking for the answer. When you're dealing with design, the main objective is to come up with something that works; however, you're not really told how to do so. So you have to apply your knowledge and experience to get a rough idea, piece it together, then analyze it to make sure it actually works; if it doesn't, repeat the process with a better idea of what does and what doesn't. It can get a bit touchy-feely about where to start, but the experience does help you get a better idea and your initial guesses will get closer to getting a workable (and more efficient/elegant) solution.
I suppose one could argue that I'm alluding moreso to a "craft" than an "art", but that's not entirely true either. While it's true that the most efficient designs are often visually unappealing, there's nothing preventing an engineer from making something look better while still having it stand upright; there are many times an engineer has to work around the asthetic design requirements of the building, and that can require one to be rather creative.
---
And all of this leads to something I think many people have to realize:
Art and science do NOT have to be mutually exclusive.
If anything, they complement eachother extremely well; engineering design is the perfect place to exercise this. A building can look outstanding, but it has to stand upright as well. So an architect designs the building's overall look, then an engineer comes along and sorts out all the technical details like the foundations & structural members, right?
Who says the architect and engineer can't be the same person?
While it's generally not true, there definitely are several cases where they are the same person. Having knowledge & experience in both fields is a huge asset, because one can design something which both looks great and will stay standing at the same time.
---
It's true that engineering quite often is focused on getting something which works rather than something which is perfect. However, that doesn't mean engineering is completely devoid of any artistic merit; quite the opposite, one can argue.
After all, the latin roots of the word "engineer" are "ingeniare" and "ingenium". The former meaning "to contrive, devise", the latter "cleverness"; the strong resemblance of both roots to the word "ingenious" should also be readily apparent. All of those terms imply a sense of creativity, something which is at the heart of all arts.
The only difference is that an engineer has to more than come up with something creative.
He or she has to come with something creative which works.