What P040E usually means
P040E is the companion-side version of the EGR temperature sensor circuit fault family. Instead of focusing on sensor A, it tells you the controller is unhappy with sensor B, which many diesel and some late gasoline platforms use to compare temperature behavior across the EGR path. That matters because a dead or erratic B sensor can make the ECU distrust cooler efficiency, EGR flow plausibility, and regeneration-related thermal modeling even when the valve and cooler hardware are mechanically intact.