же is one of the strangest things in all of Russian.
Among its other meanings, it can convey a sense of sameness.
It works in structures like this:
[answer word] + же = the same [answer]
"Answer word" is a term for all those words that come from similar roots and begin with т, and answer a corresponding question word, beginning in к
как -- так
когда -- тогда
куда -- туда
где -- там (Note that г and к are voiced and unvoiced brethren, and it is followed by a voiced д, which affects the sound before it)
(что) кто -- то(т)
какой -- такой
From here we get phrases like:
как - in what way? -------так же - literally: in the same way (used as: "also" or "as well")
что/кто - what/who ------ тот же - the same _____ (or the "same thing" when in the neuter)
какой - what kind? ------ такой же - the same kind
The usage of то же is as follows:
У меня та же книга.
Я увидел тот же фильм.
The word то is used as a modifier of книга, and фильм so it matches them in case
If there is no noun, then you are talking in the abstract about the "same thing":
"Ты думаешь о том же, о чём и я?" - Are you thinking about the same thing, about which I am? (In these cases, тот is put into the neuter singular, and again, still changes for case)
"Same time, same place" - На том же месте, в тот же час
The phrase "там же, тогда же" seems to be said as well.
Your next thought might be that "тогда же" would mean what you want, however:
1. This just means "the same time", not "at the same time"... If that makes sense.
2. I haven't ever seen тогда же, it is, at best, uncommon.
When talking about time (except for weeks), в + acc is always used. Often in English we just say the word for a time and it floats around our sentence but Russian much more commonly threads the time-word through a preposition, like when we say: "on sunday", "at one o'clock", or "in 1999"
в то же время quite literally translates to "at the same time"
Here's some magnificent syntax for ya:
Её чувство было настолько же случайно в выборе предмета, насколько в своем источнике отвечало властной потребности инстинкта, который не знает самолюбия и только и умеет, что страдать и жечь себя во славу фетиша, пока он чувствует впервые. Б. Пастернак, Детство Люверс.