It is true that people should know the topic, but however, not everybody else would be able to remember the whole string. Even when they search for a keyword for the subject, it may show alot of results, which will make it harder for them to find the correct topic that they are looking for. On the other, if you search by the TOPIC_ID, it will not show as much as the keyword itself, just the numbers itself will show.
We are a technical staff team and we want to be able to assist the people by the order of the TOPIC_ID. The order of the TOPIC_ID will determine the priorities of our replies. It is really hard to explain, but we believe that the TOPIC_ID would be a useful tool for us. Thanks<

Huw, I think that's what L3recher meant when he said:

not everybody else would be able to remember the whole string

An alternative method, L3reacher, that would save you the headache of editing search.asp would be to add a small form to inc_header.asp with a single text input where members could enter the TOPIC_ID of the topic they were looking for and you could then, upon submission, use javascript to construct and redirect to the relevant URL.
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Hmmm... how much of a coding will this little form take, since I am not a programmer. Will the textbox on the header act as a topic search field?? I can try to go online and get some help tutorials on creating this form.<

In fact, the easiest way to do it would be to use get as the form's method, topic.asp as it's action and TOPIC_ID as the name of the text input. Doing it this way, the form will submit to topic.asp with TOPIC_ID in the querystring, no need for an additional handler to process the form and redirect to the appropriate topic.
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Would it be something like this for the form?
<form action="topic.asp" method="get">
<input name="TOPIC_ID" />
<input type="submit" />
</form><