Too Exhausted to Meditate

How do I meditate when I’m exhausted 5 days a week?
I have started a new job in a role I wanted, at a company I wanted to work for.  Thing is, besides for a half hour lunch break where one just has time to eat, I work non-stop until clock-out at 5pm.  Its not feasible to relax and find a state of Zen at work because there are always 100 things to do within a tight deadline.  When I reach home, I pretty much eat then sleep, resting for the next day to come.  BTW I exercise regularly and my vital signs are excellent.
I end up waking up as late as possible because my body is still tired from the previous day’s work.  Prior to starting this job, I was temporarily unemployed.  During that time however, it was much easier to meditate.  I enjoy being in a state of stillness, and I used to do it every day, but now for 5 days in the working week I just want to sleep.  If I try to meditate, my body falls asleep because both my brain and body want to switch off from fatigue.  Deepak, how can I meditate when I’m exhausted 5 days a week?  I’m young and just started my career, so leaving immediately and doing something less taxing is not the short term solution I’m looking for.  In my career (finance) high workloads & tight deadlines are the norm.  I don’t plan on doing it forever, but for now I just want to know: How can one maintain stillness from meditation in the face of fatigue and modern day stress?