The ESP management light & abs lightcomes on to inform you that the traction control system & abs is not working correctly and it stores a fault code in the ECU with information on what is wrong.
You can only access this information via a diagnostic device.
I advise you to take your car to a VW main dealer or specialist to have a real time diagnostic check done so a full diagnose can be given cost depends on labor rate.
It could be a failed part on the ESP system or just a software issue that will require an update.
The most common issues with the ESP system is failed wheel speed sensors