Remove/Hide Terminal window from custom Application List entry

Question

First off, apologies if this is not the right place for this specific question, but new to both the site and the OS in question.

-System Details- OS: Xubuntu 14.04 (xfce)

Question: I have manually added a new program to my Applications List, by creating a new file with the following script:

[Desktop Entry]
Version=1.0
Type=Application
Terminal=false
Icon[en_AU]=/home/username/programdir/programexe.gif
Icon=/home/username/programdir/programexe.gif
Exec=/home/username/programdir/programexe
Name[en_AU]=ProgramName
Comment[en_AU]=Program Name
Name=ProgramName
Comment=Program Name

This file is than placed in /usr/share/applications

This program requires SUDO access to launch correctly, which I was able to accomplish by editing the following lines:

Terminal=true
Exec=sudo /home/username/programdir/programexe

This causes a Terminal window to open where I can enter the SUDO pass, and allow the program to launch fully.

Issue: Once the Terminal window opens, it remains open and will only close when the program is shutdown.

I have tried setting the line "Terminal:true" to "Terminal:false", but this effectively stops the program as the Terminal window will not launch during startup for the SUDO pass entry.

Is there a way for me to get the Terminal window to close once the pass has been entered, so that it is not constantly present?

Thanks in advance.

Best Regards, TH