A Talent Test combines a hero's Attributes and her Talent Prowess for determining the outcome of an action. She simultaneously proves her physical capability and makes use of personal experience in the appropriate field.
To pass a Talent Test, a hero rolls three consecutive Attribute Tests. If the hero has experience in the Talent in question, the TP Value can be used to lower either or all of the respective rolls. Thus, Talent Prowess can be regarded as some kind of "emergency account of free Attribute points." Of course, you cannot spend more points of TP than the total amount of TP your hero has in this "emergency account" (i.e., the respective Talent).
Elgor tries to get past the guards unnoticed. The Sneak Talent requires Tests against the Attributes Courage, Intuition, and Agility. His Attribute Values are: CO 10, In 11, and AG 13. His Talent Prowess in Sneak is 7.
The Courage Test comes up 12. Without his 7 points of Talent Prowess, Elgor would have failed the entire Test right with the first Subtest. However, he is able to spend 2 points of TP, making up for the difference. He has 5 points of TP left.
His Intuition Test comes up 4. That's a neat success.
Elgor's player rolls a 17 on the Agility Test. This means he has to spend another 4 points of TP to make the Test work.
In the end, Elgor's Sneak Test is successful, with even 1 point of TP to spare. Should he need to Sneak again, however, he would start again with his full total of 7 points of TP.
Difficulty Increases and Decreases to Talent Tests: Talent Tests may be made more difficult (i.e., receive a Difficulty Increase) in special circumstances. A Difficulty Increase is indicated by a positive number, e.g., a Sneak Test +4. A Difficulty Decrease is expressed by a negative number, e.g., a Sneak Test -2. In all such cases, the hero's TP in the corresponding Talent is automatically modified before the individual Tests take place.
Had the required Talent Test been a Sneak Test +4, Elgor would only have been able to spend 3 points of TP; had it been a Sneak Test -2, he would have been able to spend 9 points of TP.
Effective Encumbrance (EEC): A metal-clad warrior is going to find it a lot harder to Sneak than a lightly-armored burglar. Thus, each type of armor comes with a value for Encumbrance (EC), telling you how much this armor restricts your hero in certain situations. The higher EC is, the harder actions like climbing, swimming or fighting in this type of armor get. Effective Encumbrance (EEC) is a value taking into account the actual effect of armor on the various Talents: heavy armor is more bothersome to an acrobat than to a drover. EEC is a function of your hero's Encumbrance by armor type worn and the actual measure of agility needed to use the Talent in question.
Caution: Armor is not the only factor influencing EEC! The items carried by your hero (as represented in your Inventory) also count towards EEC.
A negative total value of EEC is not in any way relevant for gameplay.
The Effective Encumbrance of the Hide Talent is: EEC = EC-2. Thus, if Elgor were wearing a long chain-mail shirt (EC 4), his Effective Encumbrance is calculated like this: EEC = 4 - 2 = 2. If, however, he were wearing only normal street clothes (as would befit a burglar), EEC equals 1 - 2 = -1 (=0).
Effective Encumbrance is automatically subtracted from your hero's Talent Prowess just prior to rolling any Test. The final amount of TP left is called Balancing Value.
Due to these modifications, TP may actually drop to below zero. In very rare cases, a hero might have negative TP in a Talent to begin with. In all cases of TP below zero, the hero needs to add this amount to all of her three Subtest rolls (while still trying to beat her Attribute Values); thus negative TP always lead to Difficulty Increases on all three Tests.
All of this information is mainly intended to help you understand the TDE rules better. While playing a TDE Browser adventure, all these calculations will automatically be done for you.