Think about how you can mathematically describe the car's features so that every car is different. Maybe every car has a different size of wheels? Maybe the distance from the door handle to bottom of the side window is a unique characteristic for every car? Maybe every car's proportion of front side window's to rear side window's width is an individual feature of that car?
You probably can't answer yes with 100% confidence to any of these quesitons. But, what you can do, is combine those into a multidimensional feature vector and perform classification.
Now, what will be the crucial part here is that since you're doing manual feature description, you need to take care of doing an excellent work and testing every step of the way. For example, you need to design features that will be scale and perspective invariant. Here, I'd recommend reading on how face detection was designed to fulfill that requirement.
Will Machine Learning be a better solution? Depends greatly on two things. Firstly, what kind of data are you planning to throw at the algorithm. Secondly, how well can you control the process.
What most people don't realize today, is that Machine Learning is not some magical solution to every problem. It is a tool and as every tool it needs proper handling to provide results. If I were to give you advice, I'd say you will not handle it very well yet.
My suggestion: get acquainted with basic feature extraction and general image processing algorithms. Edge detection (Canny, Sobel), contour finding, shape description, hough transform, morphological operations, masking, etc. Without those at your fingertips, I'd say in that particular case, even Machine Learning will not save you.
I'm sorry: there is no shortcut here. You need to do your homework in order to make that one work. But don't let that scare you. It's a great project. Good luck!