Voltage drop - Diode reverse biased
You claim your second diode is reverse-biased. You can only make this assertion if it doesn't conduct current, and not because its terminals are switched.

Note that for forward-biased diodes, the forward-biased junction potential is the voltage drop from P to N, meaning that the voltage drop from N to P is the negative of this. If you look at your calculations, then you will see that you used the same polarity for both!

EDIT:

Please note that when you're assuming that the diode is forward-biased, the resultant current you calculate through the diode (from P to N) should be positive; if its negative, then your initial assumption that the diode is forward-biased is incorrect, and therefore it is reverse-biased (and hence doesn't conduct current). It was mentioned in the comments that OP may not know about this, so I provided clarification.