If by "packet radio" you mean the common AX.25 kind used by APRS for example, you can probably forget about it. Otherwise you'll need to use HF, and also find an appropriate mode since there's nothing quite like packet on HF which works reasonably well.
A VHF or higher direct link will be difficult. The radio horizon in miles of an antenna at height h feet is approximately:
$$ 1.23 \cdot \sqrt{h} $$
You say you have a 100 ft tower on each end, so that's $2 \cdot 1.23 \cdot \sqrt{100} \approx 25 $ miles. To make that work you'll need much taller towers, or perhaps you can place one or both of them on a mountain peak.
You might also see How do I make a RF propagation map for a repeater?
Alternately, you could have a number of intermediate stations relay the signal. For packet radio this is called a digipeater.
If you want a direct link, you'll have to resort to something fancier. Troposcatter would be fun, but we can probably rule that out due to the very high transmit power that would be required. A communications satellite would be too expensive.
So that means HF. At distances of 100 miles, NVIS propagation is a good bet. You can play with VOACAP to get some idea, but the strategy is probably 40 or 80 meters with a low dipole.
You can pretty reliably communicate at these distances with such a setup, but getting packet radio specifically to work will be difficult. Packet isn't a good modulation to start, and on HF it's even worse.
There are some people running packet on HF, mostly 20 meters. It runs at 300 baud, and if you ever try it you'll find somewhere between 70% and 100% of what you hear are retransmissions.
Of course this isn't HF's fault: it's just that packet is horrible. The FreeDV modem is a better example. It transmits a 1400 bit per second digital voice codec (Codec 2) with a reliability that's around the same as SSB. That means we can use the SSB mode in VOACAP to get some reliability prediction. For me looks like with a 100W transmitter and a good dipole, about 90% is achievable at night, and 60% during the day. With better antennas, more power, or a lower bitrate, you can get those numbers higher.
Of course you want to send data, not digital voice, so you'd either need to use the FreeDV modem but send something other than Codec 2 over it, or find some other mode. There are plenty of HF data modes, but none of them are quite like packet.