Here is a step by step guide on how you can update the firmware on your e series switch. In this example we will use TFTP on a standard windows 7 PC. Give the switch an IP address, use TFTP and the copy command from CLI to do so.
First lets give the switch an IP if it already has not. CLI onto the switch and enter
once in switch configuration,select IP configuration and change the IP mode from DHCP to static and assign it an address in your range.
Once done, save the configuration and return to CLI. Now on a pc that is on the same IP range download and install a TFTP server. I used the cisco ftp server as its nice and simple.
Once installed copy the latest firmware to the folder you will allow to be used for TFTP as seen here.
Now back to the cli of the switch issue the command below, changing the name of your firmware and your source ip of the TFTP server.
copy tftp flash 172.16.254.195 H_10_83.swi
Once updated issue the reload command and the switch will boot with the latest firmware.