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I am trying to write the following $T_E$ but it appears in italic font. I tried also $textT_E$ but LaTeX gives me error.

Depending of if you are actually writing math or text:

 documentclassarticle

begindocument
$mathrmT_mathrmE$ or TtextsubscriptE

enddocument

The following examples illustrates several possible solutions.

documentclassscrartcl
usepackageamsmath

newcommandtestlineText $mathrmT_mathrmE$ or $textT_textE$ or $textupT_textupE$ or Ttextsubscript E

begindocument

testline

itshapetestline

sffamilyupshapetestline

itshapetestline

rmfamilyupshapebfseries%as before but bold 

testline

itshapetestline

sffamilyupshapetestline

itshapetestline

enddocument

Observe that some of them adopt the style and font of the text.

With the Modern Toolchain

With the unicode-math package (which I personally recommend, although not everyone agrees), mathrm is still supported for backwards compatibility, but so is the synonym mathup, and the closely-related symup.

If you use symup, you can specify a different upright font from the regular text font, and from operator names like log, sin and lim. My go-to example is setting Euler’s identity in ISO style, that is, with symbolic constants set in an upright font, with the constants e, π and i in Euler and everything else in Palatino. It’s a good example of why you might want a different upright font for math variables.

documentclass[varwidth, preview]standalone

usepackagemathtools
usepackage[math-style=ISO]unicode-math

setmainfontTeX Gyre Pagella
defaultfontfeaturesScale=MatchLowercase

setmathfontAsana Math
setmathfont[range=up/Latin,latin,Greek,greek, 
 bfup/Latin,latin,Greek,greek,
 script-features=, sscript-features=
 ]Neo Euler

newcommandupesymupe
newcommandupisymupi

begindocument
beginalign*
 upe^upi x &= cosx + upi sinx \
 upe^upi uppi + 1 &= 0
endalign*
enddocument

(If you want to do something like this with the default font, you can try either Latin Modern Roman Unslanted or CMU Serif Upright Italic. Here’s a sample of the latter:

documentclass[varwidth, preview]standalone

usepackageamsmath
usepackage[math-style=ISO]unicode-math
setmathfontLatin Modern Math
setmathfont[range=up/Latin,latin,Greek,greek]CMU Serif Upright Italic

begindocument
beginalign*
 symupe^symupi x &= cosx + symupi sinx \
 symupe^symupi pi + 1 &= 0
endalign*
enddocument

The symup command is intended to be used this way. The mathrm and mathup commands are more for words in equations, like naming variables TIME and ENERGY. Another good alternative for whole words is to use operatorname from amsmath. This formats the text like log or sin, that is, inserts spacing like 2 log x rather than 2logx.

There are similarly mathtt and mathsfup for monospaced and sans-serif letters.

You could also, for example, do newcommandTIMEmathopmboxscshape time to get TIME in small caps, with the spacing of an operator.

You can make upright math variables the default by loading the package with usepackage[math-style=upright]unicode-math.

With the Legacy Toolchain

The eulerpx package implements the popular combination of Euler math variables and Palatino text, along with symbols from newpxmath. If you want upright letters in PDFLaTeX, this in my opinion is the most attractive package for them.

The cfr-lm package makes upright italics easily available; with this package, you could write DeclareRobusTCommandmathui[1]mboxuishape #1 to get upright italics. The example I gave earlier with scshape for small-caps would work as well.

To format a variable name in the default font, operatorname from amsmath is a good option.

For a more complicated use case, there are DeclareMathAlphabet and DeclareMathSymbol.