What are the differences between Xbox 360E and Xbox 360S?
Looking at the Amazon page for the product, yes it does support Kinect.
Kinect Ready
Kinect makes YOU the controller. With a dedicated, specialized port, the Xbox 360 250GB is built to connect seamlessly with the Kinect sensor and have you up off the couch and into the world of Kinect in no time.
The only differences between the E and the S is the physical appearance and less ports:
In addition to its revised aesthetics, the Xbox 360 E also has one fewer USB port, no AV connector (and thus is HDMI-only), and no longer supports S/PDIF.