It doesn’t. They have their own separate absorption pathways.
Each of them can take over the job of the other, if the other is low, at least to some degree. My guess as to why E is often paired with Se, is that if Se is low to the point you need to supplement, the E may be low as a result of doing its normal work AND some of the work Se should be doing.
But there are also lots of horses who are low in one and not low in the other, so you can’t assume. But the level of E with Se supplements isn’t remotely enough to cause problems.
If he seems otherwise happy and engaged, eating and drinking well, then you could wait until things cool off and see if his energy perks up
Otherwise a basic CBC would be good, at least as a baseline if nothing else.