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With tense issues(although this technically isn't one) you have to look at the meaning and not just follow a rule of thumb stating not to change tenses.

Involving is not a verb in choice E, it's a participle, thus it does not have a tense. The robbery itself is "involving" bank robbers and hostages, whether the robbery is actually still going on or not, you get what I'm saying(although again, there's no tense issue here)? So in that sense the sentence makes sense, so you can't eliminate any answer choices with "involving".

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I chose 'D'.

I also think that the answer should be option D though i was confused between D and E.

Here if you see both the sentences are in past tense. and therefore involved is better than involving.

Guys, am i correct here. Experts please respond.

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IMO (E)

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The correct answer should be D. Please see the explanation below:

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I may be wrong guys but if in choice E, involving modifies the negotiaters then there should be a comma before involving.

Correct me if i am wrong with my understanding

Ing modifier, Clause Can modify a whole clause , subject, action, and vice versa but

subject + ing modifer wihtout comma correctly modifies the the subject and which makes E correct as it is correctly referring to the situation.

Help pllease

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r u sure its E, coz evn i think there shud b( , )b4 involving..!!

Went for E. Came down to between D and E. Eliminated D on the point that it was wordy and that the situation was continuing till the point is was resolved, i.e. hence Involving.

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The answer should be (E).

As for the distinction between (D) and (E), the issue of verb tense comes at play. the v-ing action (involving) sets the background whereas the main action in simple past (resolved) is on the foreground. The sentence focuses on the event -- hostage negotiators finally resolved a situation. But what is the situation? Okay, here I'm gonna provide background information: the situation involving bla bla. Therefore, the v-ing form in (E) is justified, whereas the past tense "involved" in (D) fails to clarify the temporal and logical links of these two events/actions, both in simple past.

Here's an example sentence, courtesy of Ron
OG-12 QUESTION 95, correct sentence as below:
The peaks of a mountain range, acting like rocks in a streambed, produce ripples in the air flowing over them; the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, is known as “standing waves.”

See here for Ron's explanation: http://www.beatthegmat.com/the-peaks-of-a-mountain-range-t12830-15.html

Also, regarding the point that Brian raised, "no comma + v-ing" form is a noun modifier that modifies the closest preceding noun,i.e."situation", so there's no problem in (E).

"no comma + v-ing" is a noun modifier
"comma + v-ing" is an adverbial modifier, unless there is no complete clause preceding it (e.g. an official sentence: "Neuroscientists, having amassed ... in the past 20 years, are now drawing solid conclusions ....")

Here is a similar problem testing "noun VERBing" vs. "noun that VERB":
http://www.beatthegmat.com/united-states-air-force-officials-a-cannon-t65070.html

Notice why in the above question "a cannon shooting dead chickens at airplanes has proved helpful" is wrong. You may want to check out "reduced relative clause" mentioned by niksworth.

IMO D
In option D that correctly modifies the situation.