My 260E does exactly the same thing. Only difference is that during the first crank in the morning it starts up fine. but once the car is warm and i try to restart it afterwards, the first crank is always unsuccessfull. it starts and dies right away . i almost always have to crank it again and it starts up fine on the second one.
Reading some previous posts people suggested it could be vapors in the fuel lines accumulated, etc etc. there were many theories behind it which, when I added up, were costing anywhere from a 1000 to 3000 dollars. I really didn't think trying to get away from cranking twice was worth that much and all the trips to the mech. to try to troubleshoot all the parts. Hence I installed a remote starter and now I just remote start it before I'm entering the car. The first time always fails but the remote start senses that and starts it up again. so by the time i'm in the car, it has already started
The rest is your choice. good luck with it. But from what I've read a lot of 300E owners had this problem and couldn't pin point the problem area. It was basically just changing parts till you get lucky and the problem goes away.