Does it matter which goes in the glass first when having half/half tea

TL;DR = The sweet tea takes longer to cool down because there is a lot more stuff in it to get cold.

When cooling unsweetened tea, you are cooling almost pure water (the tea solids are negligible). A 12 ounce glass of unsweetened tea has about, you guessed it, 12 oz (by weight) of liquid to cool, or 340 grams (mass).

Southern-style sweet tea (if this is the "sweet tea" you are referring to), has a 2:1 ratio (by volume) of tea to sugar. A 12 ounce glass of sweet tea has 12 oz (by weight) of tea, and 5-6 ounces of sugar (by weight - 8 oz of sugar by volume = ~7 oz by weight). This puts the total weight of the beverage at 18 ounces or 510 grams (by mass).

The sweet tea, in this example, has 50% MORE mass than the unsweetened tea! This extra mass will take more time to cool down, because there is a lot more STUFF to get cold. It occupies the same volume, but there are a LOT more molecules to chill.

Compounding factors:

• Heat Capacity vs. Specific Heat: A detail to this is that a solution of sugar and water has a lower specific heat (by MASS unit) than pure water, so the total heat capacity of the sweet tea is not quite 150% of the heat capacity of the unsweetened tea, but somewhere between 100% and 150%. Intuition would put it somewhere in the 130%-140% range. Read the physics.SE question linked above for some details on that calculation. Rest assured, however, that the heat capacity of the sucrose solution is higher than pure water.
• Conductivity: I've ignored the thermal conductivity of the solution, since I'm assuming that the stirring in the tea makes the small conductivity differences between the solutions negligible, but that calculation could be done as well.
• Convection: Unstirred sweet tea will experience less convection than unstirred unsweetened tea. In the unstirred sweet tea, dense sucrose solution will remain at the bottom while the cold water from the melting ice will sit on the surface (you can actually see this visually if the tea is sufficiently colored). This slows cooling by slowing the mixing of the cold liquid with the warm liquid. In unsweetened tea the cool liquid will sink the bottom, promoting convection and self-mixing. However, convection is a side-issue to the primary point, the total heat capacity of the beverage.

And as a final note, explanations like this really make it obvious how annoying it is that US measurements use ounces for both volume AND weight.

I've never known the science behind it, but water heated in a microwave oven makes horrible tea and coffee. You need a kettle.

The standard British teabag-and-mug technique (as opposed to the loose-tea-and-teapot technique) is:

• put cold tap water in kettle
• turn kettle on
• put teabag in mug
• allow kettle to come to full boil
• fill mug with freshly boiled water
• leave for 30 seconds or so
• remove teabag with a teaspoon; give it a little squeeze for extra flavour
• stir in sugar (optional)
• add milk (optional)

Scientific rationale:

• The water needs to be as hot as possible to extract all the flavour: boiling water can't get any hotter
• Remove the teabag before adding milk or sugar because otherwise some of the milk/sugar will be removed along with the teabag
• Stir in sugar before milk because it will dissolve more efficiently in hotter liquid
• Milk last because you can judge the colour more easily

However

I've seen people claim that the water should be cooler than boiling, because the boiling water destroys subtle flavours in the tea. That may be true, but I suspect that teabag-grade tea just isn't that fine; in any case the conventional wisdom is boiling water for tea, below-boiling water for coffee.

A note on strength and timing

The longer you leave the teabag in, obviously, the stronger the resulting tea. Experiment and find your preference. 30 seconds seems to be about right for a typical British tea drinker, and a typical British teabag.

However, it should be noted that a typical British teabag isn't really intended for the one-mug method -- it's a size originally sized for teapots, and you're likely to get at least two mugfuls from one teabag, if you make tea in a pot and top up with boiling water after pouring.

You could, in theory, re-use a teabag to make a second mug of tea, but teabags are so cheap that hardly anyone bothers.

The teabags found in some cafes, smaller and with a string for pulling them out of cups, need a longer steep, since they contain less tea.