Haskell, 18 bytes

f a=max(sum a)(-1)

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APL+WIN, 6 bytes

Prompts for a vector of measurements and uses ¯1 to indicate tamper.

¯1⌈+/⎕

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Charcoal, 6 bytes

Ｉ⌈⟦±¹Σ

Try it online! No verbose version because it can't do implicit input. Uses -1 as the tamper value. Explanation: Same as everyone else.

        Implicit input
     Σ  Take the sum
    ¹   Literal integer `1`
   ±    Negated
 ⌈⟦     Take the maximum
Ｉ       Cast to string
        Implicitly print

Desmos, 26 bytes

f(a,b,c,d)=max(a+b+c+d,-1)

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Google Sheets / Excel, 17 bytes

Expects input in A:A

=MAX(SUM(A:A),-1)

PowerShell, 25 bytes

%{$s+=$_};($s,-1)[$s-lt0]

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Sums the values in ForEach-Object (%) loop, then uses an array indexed with a truthy/falsy value to avoid if/else.
Input comes from the pipeline.

Ruby, 19 bytes

->a{[a.sum,-1].max}

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05AB1E, 3 bytes

O®M

Uses -1 as tamper value.

Try it online or verify all test cases.

Explanation:

O    # Take the sum of the (implicit) input-list
 ®   # Push -1
  M  # Push a copy of the maximum value on the stack
     # (after which the top value is output implicitly as result)

Vyxal 3, 3 bytes

∑⑧Ġ

Vyxal It Online!

∑⑧Ġ­⁡​‎⁠‎⁡⁠⁣‏‏​⁡⁠⁡‌⁢​‎‎⁡⁠⁢‏‏​⁡⁠⁡‌⁣​‎‎⁡⁠⁡‏‏​⁡⁠⁡‌­
  Ġ  # ‎⁡max(                      )
 ⑧   # ‎⁢    -1,
∑    # ‎⁣       sum(implicit input)
💎

Created with the help of Luminespire.

<script type="vyxal3">
∑⑧Ġ
</script>
<script>
    args=[["[10,10,10,-10]"],["[-5,-7,24,0]"],["[-10,100,-10,-10]"],["[10, -1, -5, -4]"],["[6, -7, 8, -8]"],["[6, -9, 8, -8]"]]
</script>
<script src="https://themoonisacheese.github.io/snippeterpreter/snippet.js" type="module"/>

Python 2,  29  26 bytes

-3 bytes by l4m2.

Uses -1 as the tamper value.

print max(sum(input()),-1)

You can do  27  23 bytes if functions are allowed.

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JavaScript (Node.js), 27 bytes

x=>(e=eval(x.join`+`))<0||e

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e

Python 3, 63 Bytes

a=sum(map(int,input().split()));print("T")if a<0 else print(a)

Breakdown:

a=sum(map(int,input().split())) - Get input, convert to integer, sum

print("T")if a<0 else print(a) - Check for tamper, otherwise print

Can definitely shorten, but a decent solution nonetheless