After "Number" on every line:
sed "s/.*Number/& $PARAM/" log.txt
After "Number" on the last line:
sed "\$s/.*Number/& $PARAM/" log.txt
After "Number" the last time it appears in the file:
sed "/Number/!b;:a;\$!N;/\n.*Number/{h;s/\n[^\n]*\$//p;g;s/^.*\n//};\$!ba;s/^\(.*Number \)/\1$PARAM/" log.txt
Explanation of the last version:
/Number/!b - if the line doesn't contain "Number" branch to the end of the script and print the line
:a - loop label "a"
\$!N - if it's not the last line of the file, append the next line to the end of the contents of pattern space
/\n.*Number/{ - if pattern space includes "Number" after a newline then
h - copy pattern space to hold space
s/\n[^\n]*\$//p - delete the part after the newline and print the remainder
g - copy hold space to pattern space
s/^.*\n//} - delete the part before the newline, end if
\$!ba - branch to label "a"
s/^\(.*Number \)/\1$PARAM/ - add the contents of the variable after "Number"