How do I add an expand/collapse transition?
http://jsfiddle.net/Bq6eK/215/
I did not modify your code for this solution, I wrote my own instead. My solution isn't quite what you asked for, but maybe you could build on it with existing knowledge. I commented the code as well so you know what exactly I'm doing with the changes.
As a solution to "avoid setting the height in JavaScript", I just made 'maxHeight' a parameter in the JS function called toggleHeight. Now it can be set in the HTML for each div of class expandable.
I'll say this up front, I'm not super experienced with front-end languages, and there's an issue where I need to click the 'Show/hide' button twice initially before the animation starts. I suspect it's an issue with focus.
The other issue with my solution is that you can actually figure out what the hidden text is without pressing the show/hide button just by clicking in the div and dragging down, you can highlight the text that's not visible and paste it to a visible space.
My suggestion for a next step on top of what I've done is to make it so that the show/hide button changes dynamically. I think you can figure out how to do that with what you already seem to know about showing and hiding text with JS.