What was found
DURING FULL THRUST TAKEOFF OAT AT 13 DEG, NR 2 ENG EXCEEDED MAX EGT LIMIT, RED EGT WARNING LIGHT ILLUMINATED & EGT 947 DEG FOR 5 SECONDS. ON CLIMB NR 2 ENG RAN 105 DEG HOTTER THAN NR 1 AT 877 DEG. AT CRUISE NR 2 ENG 100 DEG HOTTER THAN NR 1 AT 716 DEG. MX REQUESTED BOTH PMC'S BE SWITCHED OFF, THROTTLE SPLIT WENT FROM NR 2 THRUST LEVER BEING FORWARD OF NR 1 BY 1.5 INCHES TO A SPLIT OF 2.5 INCHES. DECLARED EMERGENCY, DIVERTED. FOUND NR 2 ENG MAIN FLEX SHAFT BROKEN BETWEEN VARIABLE BLEED VALVE GEAR MOTOR & BLEED VALVE STOP MECHANISM. R&R NR 2 ENG MASTER VBV GEAR MOTOR AND STOP MECHANISM, EGT PARAMETERS GOOD ON ENG RUN OPS CHECK. VENDORS TEST OF MASTER VARIABLE BLEED VALVE GEAR MOTOR, NO FAULT FOUND.