Bash shell script to locate and remove substring within a filename
With bash only: 

for filename in *; do
    if [[ "$filename" =~ (.*S[0-9][0-9]E[0-9][0-9]).*(\....)$ ]]; then
        echo mv "$filename" "${BASH_REMATCH[1]}${BASH_REMATCH[2]}"
    fi
done


Remove the "echo" when you're satisfied it's working.