So here's the funny part....
I looked it over... took a breath and started talking my way through the problem. He agreed that it was a difficult one and told me to take my time. I was talking about subnet at one point and he asked which class it was to which I replied it was class B. He agreed and confirmed that I was correct to the other two panel members. After some more thinking on it I arrived at the following answer:
First available IP: 145.36.0.1 with a subnet of 255.255.252.0
Second available: 145.36.0.2 with a gateway of 145.36.0.1 and a subnet of 255.255.252.0
....exactly what you just said.
He said I was wrong and asked the other panel members (Head of HR and company President) to borrow the dry erase board in the meeting room to demonstrate how to arrive at the proper answer. He broke down a lot of stuff and in the end he arrived at: 145.36.4.1 and 145.36.4.2.
Now, at first I wasn't going to argue with him in an interview because I was already stressed out enough by other situations (turns out this 'expert' they brought and I have a past and he was the LAST person I thought I would see when I walked in) and the last thing I wanted was to be wrong TWICE if you get my drift. I need to send a thank you email to all three and I plan to double and triple check my answer before I even bring up the topic of being wrong again because if it turns out I was indeed wrong I'd rather that not ever come up again. lol I feel like I was right though and if in my email I give them the correct answer and mention it was indeed the first answer I gave suddenly I look like a friggin genius. I know this is a very delicate subject so that's why I wanted some input from others who are in-the-know.