Really this isn't just anxiety about failing, it's anxiety about having to tell people I failed, study for months again, take it again, and then wait forever again with the possibility of not passing AGAIN.
That's why it's too hard to just tell myself to calm down!
Try not to stress about it. The repercussions for failing aren't
that bad unless its tied to your employment. Otherwise having to wait another 6 or 12 month for a licence, or adding two letters after your name isn't the end of the world. Trust me, no-one will hold a failure against you (unless your employer requires it). Remember that 80% of engineers never even try to take the test. You've already accomplished a lot just to get to this point.
The loss of time due to restudying can be a drag, but it can make you a better engineer in the future by potentially improving your background knowledge and work habits. Years from now, you won't even remember the loss of time.
Taking the exam again in-and-of-itself is no bid deal. One day where you spend eight hours doing math and engineering, pfft. That's just like another normal day at the office.
I'm not gonna lie though, having to go through the wait for results again sucks! I'm so glad I'll never have to do that again.
But's on the whole, it could be a lot worse.
Here's my advice:
Step 1: Go to gym, exercise away the anxiety. After studying for the exam for a couple months, you should still have free time in your schedule to do so.
Step 2: repeat step one until you feel better or get the results
Step 3: continue to destress at the gym regardless of passing or failing. It's better for your health in the long term.