The ModBus protocol does not support the transmission of strings but as Juraj wrote above you may store the contents of your string in several 16bit holding registers.
BTW: ModBus TCP is not the default type, if you just write ModBus people usually expect you to mean ModBus RTU.
So do you know if is possible to send one complete string (10 char) to the kepware? like "ABCDEFGHIJ"
Is the string length fixed? Do you control the software that receives this "string"? Is the Kepware a client or a server in the ModBus TCP terms?
If not or if you know other way/protocol to send those two variables by Ethernet shield, please let me know.
Probably the best known protocol today is HTTP. I think it's more important what other protocols your Kepware device understands. Unfortunately you forgot the link to that product's datasheet/manual.