Download and install Entware package as described in [https://github.com/Entware/Entware/wiki/Install-on-QNAP-NAS]

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The entware package would be installed in the path /opt/bin

Run /opt/bin/Entware.sh which will move all the files to a saperate dir and links /opt to the target directory. This script also make all the commands installed via opkg in the user PATH

Install screen

/opt/bin/opkg --help
/opb/bin/opkg install screen

Running the screen might give the following errors initially

/var/run/utmp: No such file or directory
Cannot find terminfo entry for 'xterm-color'.

Workaround

touch /var/run/utmp; # fix missing file
export TERMINFO=/opt/share/terminfo; # set missing environment variables for TERM