I have a solid of revolution defined by two equations, and I want to generate a STL file for printing from the difference of the two equations, revolved around x=0. I can get a good visualization when I query this on Wolfram Alpha, but I cannot figure out how to download an STL of this. I know there is a way to do this via Wolfram's Development Program but I'm not sure how or if that is the best way to do this. Solutions do not have to involve WA.
The Wolfram Alpha "Data Download" feature supports STL format, but is only enabled with a Pro Account.
When I click your link to Wolfram, I see the visualization of your equations at the bottom of the page; when I hover over the image, several buttons show below it. One of them is "Data", with a download icon. This gives a number of download options. The File Format drop down includes "STL".
The best free solution I could find was to graph this (in Desmos), screenshot it, and convert it into a SVG, convert that into an OpenSCAD file, and then use that to make the STL. A similar process is shown on someone's blog here.