Have url use 'entry url name' where no template exists..?

I know this is something very basic, but i am just confused so any help is appreciated.

I have a template group named ‘news-and-media’. There is just the one index template within that.

There are currently two entries that use this template

Latest News (site.com/news-and-media/latest-news) Newsletters (site.com/news-and-media/newsletters)

On this template i have the code.. if segment 2= latest-news embed this (which is latest-news channel (summary) info) if segment 2= newsletters embed that (which is newsletters channel info)

Now initially all the News channel entries were appearing one after another on the Latest News page. However each entry is quite long, so i would like each News entry to have its own page.

So now i have setup the Latest News page to just show a short truncated summary of each News entry, with a ‘Read More’ link. I would like the link to each individual entry to be:

site.com/news-and-media/latest-news/this-is-entry-1

Now based on that, EE assumes there is a latest-news template, which there is not. I want to still use the index template, but the url for each entry would be like mentioned above. Is this possible?