Unfortunately, there is no 1-answer, "it's this..." type of answer here. When the Check Engine light comes on, the VSC light is also set, which turns this system off. This is a self-preservation mechanism, in case the reason the Check Engine Light is on can harm or effect the VSC system. So- fix the reason why the Engine Light is on, and the VSC systems will come back online.
When the Check Engine light comes on, this is the on-board computer's way of telling you it sees a problem in one of the monitored systems. Unfortunately, there are literally 100's of parts and sensors monitored in various systems, and to take a "guess" as to which part/sensor in which system is faulty, is virtually impossible. However, if you are not experiencing any drivability issues such as skipping, stalling, shifting problems, etc, then more than likely, the problem is going to lie in the EVAP (emissions control/recovery) system. Very commonly, this could be a faulty, loose or missing fuel cap or even putting fuel in while the vehicle is running can set the light. Check the underside of the fuel cap for any cracks or signs of defects that may keep the cap from sealing correctly. If there are any doubts about the inspection of the cap, replace it. Keep in mind, you will need a cap that meets OE Specs. Those "universal" or "locking" fuel caps sold at after market parts stores do not meet OE specs, and will not seal the system correctly. Check the top of the fuel filler neck for any signs of damage or debris. Check under the vehicle, around the rear areas of the vehicle, looking for any vacuum lines that have dry-rot cracks, holes or loose/missing connections. If these all check out, then the best thing to do at this point is to have the Diagnostic Trouble Codes (aka "p-codes") read from the on-board computer. These p-codes are what is used as a "starting point" for the diagnosis and will tell which part/sensor, in which system, has the fault. There isn't a Mechanic on the planet that can tell you what is wrong with the vehicle just by "looking" at the Engine Light. Every single Mechanic's first course of action WILL be to obtain the p-codes. It's standard diagnostic procedure. Once you get these p-codes you can more accurately and efficiently diagnose the problem and then make the correct repair. If my answer has helped you, please help me by leaving a rating using the stars at the top of this page or accept the answer so I may be credited. Rating or accepting my answer does not cost you extra. It allows me to be credited for my work. Please rate or accept. You can ask follow-up questions after you rate.