I'm not sure what it is but the fact that it is spreading is cause for concern and you should consider cutting off the affected areas with sterile tools. If you go this route then you need to dust the cuts with cinnamon also.
Check your light levels just to trouble shoot if it is sunburn. Also I would increase air-movement and spray with an antibiotic solution of horticultural oil, cinnamon extract and water. (Be sure the plants dry out after that application to prevent sunburn.)
Cattleyas sometimes look like this when they are underwatered and/or too hot. I seem to recall it is over 40C / 104 F where you live? I have had plants survive this, but only when I moved them into a much cooler area.
__________________ May the bridges I've burned light my way.
I havent seen this on a epidendrum, but plenty on one of my sobralias, could be a fungal disease, sun burns dont spread. In my case it was a black rot which attacked. If you cant find a copper fungicide procede with the cinamon powder as recomended
Good luck with it!