jmc

If $x$ is a solution, then $-x$ is a also a solution. Thus, we can pair all the solutions, and their sum is $\boxed{0}.$

Let $f(x)=2^{|x|}+3|x|.$ Since $f(0)=0$ and $f(4)=28,$ the equation $f(x)=18$ has at least one solution in the interval $0\le x\le 4.$ This ensures that the sum that the problem asks for is not an "empty" sum.