Eggs are very bad on car paint. The only thing that can damage the paint is the Shell though. If you leave an egg on your paint for a sustained period of time it will not come off. http://www.ehow.com/about_5318889_eggs- ... paint.html
What To Do
First, remove the shell pieces by hand to avoid further scratching. Then hose off the car with plain water. If the egg has "fried" onto your car's surface and will not come off with plain water, it is time to move on to phase two. Mix equal portions of household ammonia and white vinegar, soak a soft cloth (like a washcloth) with the mixture and hold it against the egg until it begins to soften. Gently pick at the egg with a fingernail. The commercial product "Goo Gone" or a bug and tar remover may be used instead of the vinegar and ammonia mixture, but again, you must keep the egg soaked with whatever you are using---and be patient. The only thing you will accomplish by rushing the removal process is damage to your paint job.
Your car's paint should show no trace of the egging. However, if white spots remain on the clear coat, use more vinegar and scrub with a washcloth. You may also be able to buff out any residual staining and light shell scratches when you wax your car.
I've always said if you have a problem with me then face me don't F with my car.