-Updated version for clearer wording and explanation:
SECTION 1: SPECIFICATIONS AND BASELINE VALUES
Challenger 2 base model weight = 62.5t
Challenger 2 TES/OES = 74.8t
TES total mass = 74.8 - 62.5 = 12.3t
Challenger 2 dimensions (approximate):
Length = 8.3 Meters
Width = 3.5 Meters
Height = 2.5 Meters
Base plate is roughly 3/4 the height of the hull if laid flat on the floor.
Shaving off 0.5 meters for the turret, and reducing to 3/4s we are given a height of 1.5 meters in height for the base plate.
The length of the plate can be measured as roughly 3/4 the length of the vehicle. 6.2 meters.
The thickness of the plate is known to be 40mm as seen in te screenshot above.
Therefore, for our total mass calculation, we will be using a theoretical steel plate that is 6.2 by 1.5 by 0.04
By using the formula Weight = Area x Thickness x Density, we are given the total weight of our approximated base plate.
Area = Length x Height
Area = 6.2m x 1.5m
Area = 9.3m2
We can now substitute our values into the forumla to solve for mass.
Weight = 9.3 x 0.04 x 7,850kg/m3 where 7,850kg/m3 is equal to the density of steel.
Weight = 2,952kg or 2.94 tonnes.
However, given the shape of the baseplate mounted to TES is not a perfect rectangle, we can reduce a further 5% from our total weight to account for areas where material should not exist.
5% of 2.94 is 0.14
2.94 - 0.14 = 2.8
Our total weight for one steel base plate mounted to TES is approximately 2.8t
Each side of TES has a baseplate. There are two base plates so we multiply the 2.8 by 2 to get 5.6, making the total weight of our steel baseplates on Challenger 2 OES and TES 5.6T

The Challenger 2 TES and OES mount protective armor under the crew compartment to defend against IEDs and anti-tank mines.
The total size of the mine plate can be seen taking up roughly 2/3 of the tanks total width.
2/3 of 3.5 (the width of the Challenger 2 as established in Section 1) is 2.33 meters.
It can be seen encompassing the same length as the base plate, therefore it is assigned the same length established in Section 2 of 6.3 meters.
The dimensions for our mine protection is therefore 6.3 meters long, 2.33 meters wide and 20 mm thick.
Please note that while this is Rolled Homogenous Armor, the density of the material appears to not change from that of steel, so the approximation will be using 7,850kg/m3 as a baseline.
Using the formula from Section 2, we obtain the following:
Area = 6.2 x 2.33
Area = 14.486 m^2
Weight = 14.486m^2 x 0.02 x 7850kg/m^3
Weight = 2,278.46kg or 2.27t for the mine protective underplate.
In all TES and OES vehicle modifications, there are two 40mm thick steel plates per side, mounted to the sides.
The plates height are almost exactly 1/4 the height of the baseplate.

1/4 of 1.5 (the height obtained in Section 2) is 0.375.
The length is the same as the base plate at 6.3m
The width is 40mm per plate, of which there are two per side.
Using the same formula, we can solve for total mass…
Area = 6.3m x 0.375m
Area = 2.3625m2
Weight = 2.3625m2x0.04x7,850kg/m3
Weight = 742.6KG or 0.74 tons
This is just the weight of one individual plate. There are four, per TES/OES.
0.74 x 4 is 2.96
We can reduce this value by roughly 5% again, as the bottom slopes towards the front saving us material.
20% off the total number (5% per block) is 2.96 - 0.59 = 2.36t for the bars at the bottom of the plate.
In total, with the base plate, double stack side armor and mine protection, our approximated weight is:
2.36 + 2.27 + 5.6
= 10.23
The TES modification weighs 12.3T, therefore: 12.3 - 10.23 = 2.07
This leaves you with 2.07T of weight to be added in the form of the LFP addon armor, Cage/Bar armor, Radio equipment, ASPRO-HMT and ECM.
To streamline this section, the exact same dimensions and formulae as previously used for steel will be used, however the density of steel will be replaced with 2810kg/cm^3, the density of Aluminium Alloy 7075 as pure aluminium would not be used.
Running the formula again, but with this density change provides you with 1045.32KG or 1.04t x 2 = 2.08t total for the base plates.
Mine protection remains unchanged, as does the 40mm plates at the bottom.
This provides us the values:
2.08 + 2.36 + 2.27 which is 6.71t total if using Aluminium base plates.
The Challenger 2 TES package is known to be 12.3T as represented in War Thunder. When applying our formulae to the baseplates and using steel as our material, we are provided with a value that closely matches our expectations of the weight of the TES package if certain elements are removed such as the ECM, Radio, Slat Armor, Frontal Plate Protection and ASPRO-HMT. There is 2.07T left when considering the material as steel, for the remaining equipment to be installed, which when added, would be in the approximate range of the 12.3T target.
When considering the Aluminium theory, however, we are left with close to 7T of weight to account for. We know from the March 2010 addition of Armor & Mobility that ASPRO-HMT does not weigh much:
And therefore the slat armor, ECM, LFP protection and radio would need to make up the weight of almost 7 tons which is unlikely.
Therefore, it is my belief that Steel closely matches the weight, expected of the plates and is the likely material used on Challenger 2 TES.
Thank you.