How to exit the sightless pit in Skyrim?

You can try the following (non-cheating) methods:

• Save often!
• Lower the difficulty to Novice (restore when you get out)
• Use wards as protection (as pointed out by JAD, watch out for mana cost)
• You can try to just run it till the exit
• Try stealth, or use sneak to lure enemies away one by one and rely on your magicka for healing and perhaps muffle.
• Grind mode: Keep training some magicka skill (illusion might work) until you are able to level up. Don't do so yet! Run toward the exit and level up just before you die, you will get full health when you do so. When you level up pick either Stamina (to sprint longer) or Magicka (to heal more), you could pick health but that won't help if you get surrounded.
• Be very selective with potions and make sure you use them only when in dire need. Magicka, health and stamina will automatically regenerate, but potions won't for obvious reasons.

This is a notorious pit where things start to get a bit more easy around level 15-20.

Some race-dependent methods:

• Altmer can equip Healing, cast Highborn, then continuously heal while running for the exit. However, the starter healing spell may be insufficiently powerful without a restoration potion to magnify it (try using both hands, or dual casting if you have the perk).
• Argonians can cast Histskin. Depending on equipment and level, that may be sufficient to render this fight winnable, or you can run for the exit if it seems unworkable.
• I'm uncertain whether the Imperial's Voice of the Emperor will affect the Falmer. It certainly will not work on the Chaurus.
• Nords can cast Battle Cry and walk out. Will affect followers.
• Orcs can cast Berserker Rage and either win the fight or run for the exit.
• Redguards can cast Adrenaline Rush and continuously sprint to the exit (sprinting is significantly faster than running and most enemies will be unable to catch up).

Other context-dependent options:

• Shouts such as Become Ethereal, Slow Time, and (possibly) Unrelenting Force may give you enough breathing room to run for the exit. Requires completing part of the main quest.
• Illusion spells (probably insufficiently powerful at level 7).
• Invisibility potions. The Falmer are already blind, but Chaurus are not, so this does still help.
• Fortify sneak enchantments or potions.
• Muffle enchantments or the spell (probably unavailable at level 7).

As @Nelson commented, this is an "one-way" cave: you cannot exit the way you came in.

In the Temple of Xrib zone, towards the east, there is a tower with a lift to another zone, Abandoned Cave. As the name suggests, it should be essentially unoccupied. From there you'll also find an exit.