All you need to calculate the network and broadcast addresses are an address somewhere in the network and the netmask, you don't need to know the gateway.
First, Take your network mask and convert to binary:
255.255.255.248 = 11111111 11111111 11111111 11111000
Next, Take the network address you know and do the same:
192.168.216.222 = 11000000 10101000 11011000 11011110
Now you can calculate the network and broadcast, for the network you carry out a logical AND between the known address and the netmask:
255.255.255.248 = 11111111 11111111 11111111 11111000
192.168.216.222 = 11000000 10101000 11011000 11011110
AND 192.168.216.216 = 11000000 10101000 11011000 11011000 = Network
For the broadcast, invert net netmask and carry out a logical OR between the known address and the inverted netmask:
255.255.255.248 = 11111111 11111111 11111111 11111000
NOT 000.000.000.007 = 00000000 00000000 00000000 00000111
192.168.216.222 = 11000000 10101000 11011000 11011110
OR 192.168.216.223 = 11000000 10101000 11011000 11011111
So, given an address of 192.168.216.222
and a netmask of 255.255.255.248
, you can calculate the network as 192.168.216.216
and the broadcast as 192.168.216.223
.
In your case, you say your ISP has given you 2 static IP's, this will in reality be 4 IP's, with a netmask of 255.255.255.252
it's just that two of those 4 IP's are taken up by your network and broadcast addresses.