Problems with analyzing a simple, non linear circuit
Think of it in reverse. When the diode is at its knee voltage (what you have called the breakpoint) you know that the voltage across the diode is 0.7V. Since the diode is just reaching the knee voltage you also assume that the current through it is negligible, so the voltage across R3 is zero. So, replace the diode and R3 with an ideal voltage source of 0.7V and figure out what \$V_E\$ must be in that case.